Burriss, who is also being invited to Spring Training, will earn $750,000 in 2013 if he makes the team out of camp. If he is not on the 25-man roster by June 1, the 27-year-old can get his release and become a free agent.
In 60 games with the Giants last season, Burriss batted .213. In parts of five big league seasons since 2008, he is a .243 lifetime hitter.
Defensively, Burriss has primarily played second base but can also play shortstop, third base and left field. Arbitration eligible for the first year heading into the offseason, he was sent outright to Triple-A Fresno but elected to become a free agent instead.
The Reds also signed Mike Hessman, who plays first base and third base, to a Minor League contract.
Hessman, 34, has only 109 games of big league experience spread over three teams, most recently the Mets in 2010. He's a .188 career hitter with 14 home runs. Hessman spent his 2011 season playing in Japan and all of last season with Triple-A Oklahoma City in the Astros' organization. Hessman batted .231 with 35 homers and 78 RBIs in 2012.
If he makes it to the Major Leagues, Hessman would earn $505,000. He can get a release on July 1 if he isn't on the 25-man roster by then.
The Reds also signed right-handed pitcher Todd Redmond to a one-year big league contract worth $490,000.
Redmond was acquired in the July 14 trade that sent shortstop Paul Janish to the Braves.
The 27-year-old Redmond appeared in one Major League game for the Reds despite multiple callups in 2012. On Aug. 18, in Game 2 of a doubleheader vs. the Cubs, he was the lone pitcher to start for Cincinnati last season who wasn't a member of the original five-man rotation. He allowed four runs, seven hits and walked five.
Overall in Triple-A last year, Redmond was 8-11 with a 3.63 ERA in 26 games, including 25 starts.