The outfielder appeared in 23 games for the Chicago Cubs last season and hit .250 (5-for-20) with one RBI. A career .269 hitter, Grieve was voted rookie of the year in 1998 after hitting .288 with 18 homers and 89 RBI for Oakland. He spent two more seasons with the Athletics, three with Tampa Bay and split 2004 with Milwaukee and the Cubs.
Chicago also agreed to minor-league contracts with left-handers Chad Bentz, Javier Lopez and Stephen Randolph; right-handers Agustin Montero and Tim Redding; outfielder Darren Blakely; and infielder Jorge Velandia.
Bentz appeared in four games for Florida last season and did not have a decision. Lopez was a combined 1-1 with an 11.02 ERA in 32 relief appearances for Arizona and Colorado.
Redding was 0-6 with a 10.57 ERA in seven starts and three relief appearances with San Diego and the New York Yankees.