Gregg, 30, acquired from the Florida Marlins for Minor League pitcher Jose Ceda, had 29 saves and a 3.41 ERA in 72 games last season. The right-hander has 61 saves over the past two seasons and heads into Spring Training competing for the closer's job with Carlos Marmol.
"I know Carlos Marmol is a great pitcher himself, and I just look for [manager] Lou [Piniella] to pick who he's comfortable with and go from there," Gregg said. "I'm more looking forward to winning and getting back in the playoffs and going deep in the playoffs, that's the most important thing. As far as what my expectations are, it's to come in, show what I'm capable of and see what Lou wants to do."
Gregg, who had surgery on his knee immediately after the regular season ended, began throwing earlier this month and has reported no problems.
Reliever Michael Wuertz is the Cubs' only arbitration-eligible player yet to reach an agreement. Teams and players exchange figures on Tuesday.
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.