Strasburg, 23, had a remarkable start to his major league career in 2010 but missed nearly all of last season following elbow surgery.
He is 6-4 with a 2.54 earned run average and 116 strikes outs over 92 innings pitched the last two seasons.
He hadn't had a great spring training until Tuesday when Strasburg allows one run on two hits over five innings against the New York Mets.
"He settled in last night and shows me what kind of pitcher he is," Nationals Manager Davey Johnson said on the team Web site. "He didn't overthrow. He had much better location. In a nutshell, he pitched."
Washington opens the regular season April 5 against the Cubs in Chicago.
Strasburg was the first overall selection of the 2009 draft. He made his major league debut in June 2010 and struck out a total of 32 batters in his first three games.
But he had an inflamed shoulder and was placed on the disabled list in July. By August, team officials said Strasburg had a ligament injury and the pitcher subsequently underwent so-called Tommy John surgery to repair a torn ulnar collateral ligament.
He was 1-1 with a 1.50 ERSA in five appearances late last season.