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.
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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.