Considered one of the most talented prospects in the event's 45-year history, Strasburg went 13-1 with a 1.32 ERA this season for San Diego State, leading the Aztecs to their first postseason berth since 1991.
Featuring a fastball that has been clocked at 102 mph, Strasburg leads Division I pitchers with 195 strikeouts in 109 innings. He was the only amateur on the U.S. Olympic baseball team that won a bronze medal in Beijing last summer.
Strasburg went undrafted out of high school, but some think he has the ability to go straight from college to the big leagues.
"It's tough to say right now," Strasburg said in an interview on MLB Network. "I'm just really enjoying the time with friends and family right now. We'll see what happens."
Signing the right-hander could be a challenge for the Nationals, however, because agent Scott Boras is sure to seek a record contract.
"We are thrilled to select someone with the special talents that Stephen possesses," Nationals acting general manager Mike Rizzo said in a statement. "Those talents have long been on our radar, and Stephen's domination at San Diego State and vast experiences gained with Team USA last summer have done nothing to change our thoughts about his abilities."
With the second pick, the Seattle Mariners chose North Carolina slugger Dustin Ackley, who has batted at least .400 for three consecutive seasons.
Regarded as the best hitter available, Ackley played mostly first base for the Tar Heels, but his impressive speed makes him a candidate to switch to center field as a pro.
"This is a guy we thought could be here in a short period of time," Mariners general manager Jack Zduriencik said in an interview on MLB Network. "The only reason he played first base this year is Tommy John surgery last year. We think this kid's got a really nice future for him in Seattle."
It was Seattle's highest pick since 1993, when the Mariners took Alex Rodriguez first overall.
The San Diego Padres were the first team to go for a high school player, tabbing outfielder Donavan Tate at No. 3.
A gifted all-around athlete, Tate was a baseball and football star at Cartersville High in Georgia, and he has committed to play both sports at North Carolina. He is the son of former NFL running back Lars Tate.
Only a few years ago, the baseball draft was held in virtual obscurity via conference call. This year it went prime time for the first time.
With commissioner Bud Selig announcing picks from the podium, the first round was broadcast live on MLB Network. The only thing missing was a Green Room filled with anxious prospects wearing flashy suits.
Nine of the first 12 picks were pitchers, considered perhaps the biggest strength in this unpredictable draft class.
The fourth and fifth selections were players who rocketed up draft boards late.
Pittsburgh went for Boston College catcher Tony Sanchez, a late bloomer, and Baltimore chose high school right-hander Matthew Hobgood out of California.
San Francisco took another right-hander, Zack Wheeler, out of East Paulding High School in Georgia. The Giants picked right before his hometown Atlanta Braves, who were thought to be interested in Wheeler.
The Braves then selected pitcher Mike Minor, who joined David Price and Jeremy Sowers as recent left-handers to be drafted in the first round out of Vanderbilt.
Cincinnati chose Arizona State right-hander Mike Leake at No. 8, and Detroit went for righty Jacob Turner, a Missouri high schooler.
The Nationals were the first team to have a pair of picks in the top 10. They chose reliever Drew Storen at No. 10, a right-hander from Stanford.