Lewis Yocum performed the procedure in Inglewood, Calif., in which a piece of ligament was taken from the 22-year-old right-hander's left leg and transplanted into his pitching elbow.
The Nationals said that Strasburg will be released from the hospital Saturday and begin rehab on Monday at the Scripps Clinic in La Jolla, Calif., near his home in San Diego.
"Everything went very smoothly and the reports were very good," Washington general manager Mike Rizzo said Friday night, before a game against the Pittsburgh Pirates.
"He'll start his rehab in a couple of days and we're very confident he will come back strong from this surgery," Rizzo added. "I really feel this is just a blip in what is going to be an outstanding career for Stephen."
Strasburg made his much anticipated major league debut on June 8 against Pittsburgh at Washington, when he struck out 14 batters in seven innings. He finished with a 5-3 record and 2.91 ERA in 12 starts, striking out 92 in 68 innings.
Strasburg was the first overall pick in the 2009 amateur draft from San Diego State. He signed for a draft-record $15.1 million.
In other news, the Nationals activated right-hander Garrett Mock from the 60-day disabled list Friday and optioned him to Triple-A Syracuse and transferred left-fielder Josh Willingham from the 15-day to the 60-day DL.
Mock made just one start for the Nationals this season before going on the disabled list April 11 because of a ruptured right cervical disc that required surgery. He has made five rehabilitation starts in Washington's farm system with a 5.40 ERA.
Willingham, who is recovering knee surgery, has been out since Aug. 16 and will not return this season. He hit .268 with 16 home runs and 56 RBIs in 114 games.