Musk is also chairman and a major shareholder in SolarCity.
Tesla had made an offer to buy SolarCity in June, but a deal was not certain because SolarCity had formed a special committee to review the offer.
The companies said SolarCity stockholders would receive 0.110 Tesla common shares for every share held, valuing SolarCity at $25.37 per share based on the 5-day volume weighted average price of Tesla shares as of Friday.
Based on Tesla's Friday close, the offer works out to $25.83 per share — a 3.4 percent premium to SolarCity's last closing price. (Get the latest quote here.)
SolarCity's shares, which had risen about 26 percent since Tesla first made the offer on June 21, were down 3.75 percent at $25.70 before the bell on Monday. Tesla shares were up 0.51 percent at $235.99.
In June, Tesla offered 0.122 to 0.131 of its shares for each SolarCity share.
The deal includes a "go-shop" provision that will allow SolarCity, which had market value of $2.62 billion as of Friday close, to solicit offers from other buyers through Sept. 14.
Up to Friday's close, Tesla shares were up 7 percent since the company first announced the offer.