ABOARD THE INDEPENDENCE, Lithuania—On the deck of this floating gas terminal, Mantas Bartuska awaits a tanker to pass a narrow inlet on the Baltic Sea with the first natural gas shipments from the Gulf Coast that many hope will transform Europe’s energy market.

“Soon, hopefully, U.S. gas will come,” said Mr. Bartuska, chief executive of the operator of the Independence, the gas terminal docked at the port city of Klaipeda, Lithuania.

After a yearslong effort, a tanker chartered by Cheniere Energy, an American company, left a Louisiana port this week with the first major exports of U.S. liquefied natural gas, or LNG. This shipment isn’t going to Europe, but others are expected to arrive by spring.

“Like shale gas was a game changer in the U.S., American gas exports could be a game changer for Europe,” said Maros Sefcovic, the European Union’s energy chief.

Many in Europe see U.S. entry into the market as part of a broader effort to challenge Russian domination of energy supplies and prices in this part of the world. Moscow has for years used its giant energy reserves as a strategic tool to influence former satellite countries, including Lithuania, one of the countries on the fringes of Russia that now see a chance to break away.

Some are building the capacity to handle seaborne LNG, including Poland, which opened its first import terminal last year. In Bulgaria, which buys about 90% of its gas from Russia, Prime Minister Boyko Borissov said last month that supplies of U.S. gas could arrive via Greek LNG facilities, “God willing.”

The shale boom has reshaped the world energy market over the past decade, with the U.S. emerging as a new energy exporter, and the beginning of gas exports represents a big moment in this new world. Deutsche Bank estimates the U.S. could catch up with Russia as Europe’s biggest gas supplier within a decade, with each nation controlling around a fifth of the market. Russia supplies about a third of Europe’s gas via pipeline.

Lots of competition

The U.S. faces a crowded market where a global glut is projected to keep prices low. American exports will help reduce European LNG prices by about 25% within two years, according to Goldman Sachs estimates. The U.S. will compete with Russia, Norway, U.K., Australia and others in Europe’s gas market. Germany, for example, gets half its gas and Italy a third from Russia.

Low prices also mean natural gas could compete with coal and help Europe achieve its commitment to reducing greenhouse gas emissions.

In Lithuania, officials have accused Moscow of engaging in a campaign of espionage and cyberwarfare to keep its share of the lucrative energy market.

“In Russia, gas always goes together with politics,” Rokas Masiulis, Lithuania’s energy minister, said in an interview at his office, across the street from a former KGB prison. “Russia is extremely aggressive in gas pricing and the arrival of U.S. LNG will change that.”

Bulgarian officials allege Russia bankrolled a wave of street protests in 2012 that forced the government to impose a moratorium on shale gas exploration. In 2014, Anders Fogh Rasmussen, then-head of NATO, told reporters that Russia was covertly funding European environmental organizations to campaign against shale gas to help maintain dependence on Russian gas.

Russia’s foreign ministry didn’t respond to requests for comment.

U.S. gas exports will improve energy security for its allies, said Chris Smith, assistant secretary at the U.S. Energy Department. Those include Lithuania, which was the first Soviet republic to declare independence in 1990 but remains reliant on Moscow for energy.

Until 2014, Gazprom owned 37% of Lithuania’s national gas company, Lietuvos Dujos, and dominated its boardroom, said current and former officials.

“There was no negotiation about gas prices,” said Jaroslav Neverovic, Lithuania’s energy minister from 2012 to 2014. He said Gazprom would send Lietuvos Dujos a list of gas prices, which the board automatically approved.

Mr. Neverovic said negotiations always took place on New Year’s Eve, when Gazprom would threaten to cut off supplies during winter’s coldest days. Gazprom denied setting unfair prices.

Gazprom calculated its prices using a formula the Lithuanians said was unintelligible. A copy reviewed by The Wall Street Journal showed a 773-word formula with multiple sub-clauses.

The result, according to Lithuanian officials, was one of the highest gas bills in Europe. In the first half of 2013, industrial buyers paid an average of 44 euro cents, or $0.47, per kilowatt-hour for Gazprom gas. Businesses in the U.K., which has its own gas reserves, paid 35 euro cents, EU data show.

In 2008, after Gazprom doubled Lithuania’s gas bill, the country realized “it was hopeless to negotiate with Russia,” said Mr. Masiulis, the energy minister. Four years later, Lithuania leased the Independence gas terminal from a Norwegian company, giving the country the ability to get gas outside of Russia.

Soon after Lithuania leased the ship, Mr. Masiulis said Russia fomented opposition to the deal. Moscow complained to the United Nations that the Independence would harm a 60-mile long spit shared by Lithuania and Russia, which is a Unesco World Heritage site. A U.N. mission found no negative environmental impact.

“This is how Soviet propaganda works,” Mr. Masiulis said. “If you can’t kill it, make it sound like a bad idea.”

When the Independence arrived in Klaipeda in October 2014, it was met by cannon salutes and martial music.

Vytautas Grubliauskas, mayor of the town of 160,000 people that is dotted with Soviet-era apartment blocks, led the welcoming party. Hundreds waved Lithuanian flags in a ceremony that was streamed live on national TV.

“Nobody else, from now on, will be able to dictate to us the price of gas, or to buy our political will,” Lithuanian President Dalia Grybauskaite said at the welcoming ceremony.

A U.S. diplomat read a letter from Secretary of State John Kerry, saying the Independence represented a “historic milestone” for Baltic energy security.

Last year, Lithuania began receiving Norwegian LNG, reducing Gazprom’s gas monopoly to a market share of less than 80%. In the months before the terminal opened, Gazprom lowered Lithuanian gas prices by 23% and it remained cheaper than Norwegian gas. Still, Lithuania plans to increase its purchase of Norwegian gas this year. The U.S. is next.

“The less energy leverage Russia has, the more freedom we have,” said Linas Linkevicius, Lithuania’s foreign minister, as he left for a recent U.S. trip to discuss gas deliveries. “Let’s hope it will arrive as soon as possible.”

Russian meddling has continued, according to Lithuanian officials. Last March, Lithuania expelled Russia’s consul in Klaipeda for allegedly spying on the terminal.

“You can feel that Russia is getting nervous about our terminal receiving U.S. gas,” said Mr. Bartuska, walking past the hundreds of pipes and spigots on the Independence, a 950-foot vessel.

Moscow doubtful

Chilling natural gas to minus 260 degrees Fahrenheit shrinks it to a liquid that can be stored and shipped by tanker to LNG terminals, such as the Independence, where it is returned to a gas and used to power factories and heat homes. The process is more expensive than shipping by pipeline.

Moscow is doubtful the U.S. can compete with Russian gas prices. Gazprom’s deputy chairman Alexander Medvedev said this month : “We are very relaxed about U.S. LNG, though very attentive.”

At current prices, U.S. gas delivered to Europe would cost as low as $3.60 per million British thermal units. Russian gas now costs around $4.60, on average, according to Trevor Sikorski of London-based consultancy Energy Aspects. But, he said, “If Russia wanted to chase out the U.S., they could supply gas at probably $2 in a price war.”

Mr. Medvedev said Gazprom wasn’t planning a price war. But if U.S. LNG prices did fall, he added, the company “would seek to cut its own costs.”

The first major U.S. exports left Wednesday from Sabine Pass, a terminal built on a patch of Louisiana swampland. A decade ago, Sabine Pass was planned as a gas import terminal, but the project reversed direction after the escalation of hydraulic fracturing, or fracking—the technique of using blasts of water, sand and chemicals to release oil and natural gas trapped underground.

Fracking pushed U.S. oil production to its highest level in nearly half a century and led to an oversupply of gas that drove domestic prices to a 17-year low on Thursday.

U.S. producers are now looking for customers in the saturated global marketplace. Around 90 million metric tons of new gas will hit markets annually over the next three years, equal to about a third of current demand, according to brokerage AB Bernstein.

Cheniere Energy, the operator of Sabine Pass, has signed 20-year contracts with a number of European gas companies, including U.K.’s BG Group, which was acquired this month by Royal Dutch Shell PLC, and Spain’s Gas Natural.

Lithuania’s LITGAS signed a trade agreement with Cheniere last year. Officials expect the first U.S. gas to reach their shores in coming months.

Klaipeda’s mayor, Mr. Grubliauskas, said during a recent interview at his office, decorated with photographs of U.S. naval drills in the port: “U.S. LNG is more than just about gas. It’s about freedom.”