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...