"I have always been preparing myself to be here," Suarez said Friday. "I always thought I'd get the call and it would be 'Yeah, cool.' But it's not. It was 'Wow!'"
The Giants designated right-hander Vin Mazzaro for assignment to make room for Suarez.
"We felt we needed help," Giants manager Bruce Bochy said. "He's earned this. He's stretched out and ready to go."
Suarez was 1-2 with a 2.88 ERA with the Triple-A River Cats after the Giants signed him as a Minor League free agent in December.
"You never know when the call is going to come," Suarez said. "It came when I least expected it. It doesn't matter how long I've been in the Minors. What matters is I'm here right now and I'm happy for it."
Suarez is married with two children. He said his wife was more emotional about the callup.
Suarez was originally signed by the Tampa Bay Rays in 2008, reaching Double-A in 2013. In 2014, he pitched for the Los Angeles Angels' Double-A team in Arkansas and was named a midseason All-Star.
The Giants invited him to Spring Training this season and he was assigned to Sacramento.
He's started 103 of the 109 games in which he's appeared.
"I've worked all the way up through the Minor League system and I can't ask for anything more than that," Suarez said. "I'll start out in the bullpen and we'll go from there."
Rick Eymer is a contributor to MLB.com based in the Bay Area. This story was not subject to the approval of Major League Baseball or its clubs.