Elon Musk proposed combining the electric-car and solar-energy companies that he backs, the latest in a series of financial shuffles among disparate firms of his empire.

Tesla Motors Inc., Mr. Musk’s Palo Alto, Calif., electric-car company, on Tuesday offered to acquire SolarCity Corp. in an all-stock deal valuing it at up to $2.8 billion. Mr. Musk is the chairman and largest shareholder of both companies.

Tesla shares tumbled 12% in after-hours trading following Mr. Musk’s announcement, while SolarCity shares surged 15%.

Tesla, in a letter to SolarCity Chief Executive Lyndon Rive—also Mr. Musk’s cousin—said its offer represented a value of between $26.50 and $28.50 a share, or a premium of roughly 21% to 30% over SolarCity’s Tuesday closing price of $21.19. The mothers of Messrs. Musk and Rive are twin sisters.

“This is something that we have been thinking about and debated for many years,” Mr. Musk said in a call with reporters Tuesday. “But the timing seemed to be right now” because Tesla is ramping up production of batteries used in conjunction with solar panels, SolarCity’s main business, he said. Mr. Rive on the same call said he was “very excited” about the potential deal, which still requires approval from shareholders.

Mr. Musk, who has borrowed money and shuffled funds among his companies, recused himself from voting on the deal at the Tesla board meeting at which it was approved and will do so for any vote on the SolarCity board as well, the offer letter said. Antonio Gracias, a director on the boards of both companies, also recused himself, the letter said.

Tesla said the deal is subject to approval of “a majority of disinterested stockholders” of both companies.

“You should know that the board and the shareholders will be considering this, and so while I am personally excited, I will be recusing myself from the decision-making process,” Mr. Rive said in a letter to employees. “Ultimately, the shareholders will decide.”

The acquisition aims to create a company employing nearly 30,000 people with all products renamed “Tesla” that will package electric cars, batteries and solar panels for customers, Mr. Musk said.

But it would also add to the growing complexity and vertical integration of Tesla and add an unprofitable operation to its already-strained finances. Tesla, in a huge growth effort that includes building a $5 billion battery factory in Nevada, isn’t expected to be profitable until 2020 at the earliest and recently launched a share sale to raise $1.7 billion for capital expenses.

Tesla, with a market capitalization of $32.7 billion is a much larger company than SolarCity, whose market value is $2.1 billion.

The proposal is also likely to draw further scrutiny of Mr. Musk’s dealings with multiple companies he owns and helms, and their financial viability. In addition to Tesla and SolarCity, Mr. Musk is the largest shareholder and chief executive of rocket maker Space Exploration Technologies Inc.

SpaceX in 2014 was the largest buyer of $214 million in bonds SolarCity offered.

Mr. Musk has purchased shares of both Tesla and SolarCity when they have needed capital, and secured $475 million in personal credit lines with his own shares in the companies. Mr. Musk has disclosed the risks of margin calls related to the loans that can risk destabilizing the companies’ stocks.

While Mr. Musk has called questions about the financial maneuvering “valid,” he has defended the transactions with a philosophy that he has a moral obligation to put his own money at risk alongside those of other investors backing his companies.

“I don’t think this creates additional financial risk for Tesla,” Mr. Musk said on Tuesday of the proposed SolarCity takeover. “It only amplifies the possibilities for both companies.”

Still, Tesla has burned billions of dollars in cash building expensive electric vehicles with ambitious production goals.

Tesla aims to start selling a more modestly priced Model 3 car starting at around $35,000 in the second half of next year, for which it has received nearly 400,000 reservations. “This does not impact Model 3 in any way, shape or form,” Mr. Musk said of the proposed SolarCity takeover.

Mr. Musk has attracted a cultlike following, making bold predictions that include an eventual trip to Mars. Tesla’s stock price has surged more than 500% since 2013, helping it achieve a market value of more than $30 billion, more than two thirds the current value of General Motors Co. On Sunday, he declared that Tesla’s Model S car “floats well enough to turn into a boat” while emphasizing he wasn’t recommending motorists attempt such a feat.

But Tesla’s surging stock hasn’t yet translated to profits, and investors have closely watched the company for signs of dangerous cash burns.

Tesla’s proposed takeover comes amid significant struggles for SolarCity, which has suffered stock-price declines exceeding 60% over the past 12 months and lost $283 million during the first three months of this year.

The San Mateo, Calif., company installs solar panels at residences across the U.S. The company stumbled as costs rose and it cut an important growth target by half, a move SolarCity attributed to a desire to focus on profitability.

Mr. Musk said the proposed takeover wasn’t motivated by SolarCity’s declining stock price.

SolarCity’s business model is built on leasing rooftop panels to homeowners for as long as 20 years, but owning home solar arrays can bring greater savings so many consumers are opting to buy.

SolarCity’s competition has intensified over the past year as more upstart firms began offering homeowners low-cost loans to kit out their roofs.

More broadly, the home solar industry is facing stiff headwinds across several states as electric utilities push back against policies that have made it economic for homeowners to generate their own rooftop solar power and sell excess electricity they didn’t use to the power grid.

Nevada, Hawaii and other states traditionally friendly to renewable energy efforts have dialed back their solar-power incentives payments, which are the backbone of home solar firms’ balance sheets.

Several states have significantly lowered the amount of money they are willing to pay homeowners with solar panels for their excess electricity; many more states are weighing changes to those so-called net metering programs.