Shareholders of both Elon Musk companies approved the deal last week by wide margins.
The all-stock deal valued SolarCity at $2 billion based on Tesla's closing stock price Friday. It was worth $2.6 billion when Tesla and SolarCity announced the agreement in August, but their share prices have dropped since then.
Tesla Chief Executive Musk — who is also chairman of SolarCity — wants to sell solar panels through Tesla's stores. Customers can buy them to power their homes and charge their Tesla electric vehicles.
Musk says the companies' first joint product — solar roof tiles that look like traditional tiles — should be ready for installation by summer.
Shares of Tesla, based in Palo Alto, Calif., were up 1.1% at $186.99 shortly after 10 a.m. Pacific Time.