San Francisco selected the Mississippi State right-hander with the No. 20 pick. He agreed to a $1.85 million bonus, according to a source.
"It's just an honor and a blessing to be selected by the Giants, and just getting the opportunity to play baseball for a living is just something you dream about," Stratton said. "Just the fact that they'd give me the opportunity is something I'm grateful about."
Stratton said he wanted to sign quickly with the Giants in order to begin his Major League career as soon as possible. He'll head to Phoenix for extended spring camp. After taking a break to attend his brother's wedding, Stratton will head to Oregon and short-season Salem-Keizer.
"[I wanted to] get into the system and learn everything they offer," Stratton said. "I'm just really ready to put in the work that it takes to make it."
The Giants have had considerable fortune drafting pitchers in the first round recently, their picks including Matt Cain (2002), Tim Lincecum ('06) and Madison Bumgarner ('07). Stratton singled out Cain as especially having an influence on him as a pitcher.
"I think he's an excellent pitcher," Stratton said. "He really keeps the ball down. He's just got a good demeanor on the mound."
"That's all you want as a pitcher, you want to be with a program that develops the best players and the best pitchers," Stratton said. ""Just to be alongside some of these guys maybe in the future is just an honor."
Stratton led the SEC with 11 wins and a 2.21 ERA, finishing second in the conference with 123 strikeouts. He features a four-pitch combination -- fastball, slider, curveball and changeup -- and said his fastball is his main and most effective pitch.
"You've got to pitch with your fastball," Stratton said. "That's really important to be able to get to both sides of the plate, and that's something we're really going to try and develop in the system. The secondary stuff just has to keep to keep people off balance. That's the name of pitching, to keep people off balance."
Giants fans will know Mississippi State as the school from which the team selected former great Will Clark with the second overall pick in the 1985 Draft.
"He actually called me after they drafted me and congratulated me," Stratton said of Clark. "Just the fact that a Bulldog fan like him can do that is really awesome."
Stratton's visit with the Giants this week was the first time he had visited the Bay area, and he said he was impressed with the city and AT&T Park.
But he said he won't be in town for long.
"I'm going straight to Phoenix," Stratton said. "It's time to get to work."
Jay Lee is an associate reporter for MLB.com. MLB.com reporter Jonathan Mayo contributed. This story was not subject to the approval of Major League Baseball or its clubs.