The Federal Trade Commission said on Thursday that the deal was approved. It was on a list of proposed transactions that were granted quickly because the merging partners have few or no overlaps.
Tesla said in July after it made its first offer that by acquiring SolarCity the two companies would form a one-stop shop for clean energy, offering consumers solar panels, home battery storage and electric cars under a single brand. The $2.6 billion deal was announced on Aug. 1.
Tesla shares closed down 0.7 percent at $220.96 and SolarCity shares ended 0.6 percent lower at $22.36 on Thursday.
SolarCity has come under pressure from rivals offering low-cost solar energy through large, utility-scale installations, and because some state governments have reined in subsidies that encouraged rooftop solar.
A SolarCity spokeswoman said the company hopes to close the deal by the end of the year.
Tesla has yet to file a merger-related form to be reviewed by the U.S. Securities and Exchange Commission, after which it will set a date for shareholders to vote.