Sterling has joined the Blues from Manchester City on a five-year contract for a fee which could rise to £50million.
The 27-year-old arrives in West London after a very successful seven-year stint with City during which he won 10 major honours, including four Premier League titles and the FA Cup.
Sterling is the first signing of Boehly’s tenure and the American tycoon has hailed him as a “world-class talent”.
“Raheem Sterling is a serial winner and his signing is an important step in strengthening our squad,” Boehly said.
“We are delighted for Raheem to return to London with Chelsea, and we look forward to seeing his world-class talent on display at Stamford Bridge.”