Wood, the 1998 NL Rookie of the Year who saved 34 games this year, had been the longest-tenured player on the Cubs. General manager Jim Hendry said Wood was deserving of a three- or four-year deal and the Cubs are not prepared to offer him one.
In addition to the right-handed Gregg, who was the Marlins' closer until the final month last season, Chicago also has a talented set-up man in Carlos Marmol, who could close.
"We're just in a situation -- and Kerry fully understands -- that length of deal for the kind of salary that he could command right now is not our first priority," Hendry said during a conference call.
He said the Cubs need to finish their rotation -- they hope to bring back free-agent starter Ryan Dempster -- and add offense.
"We felt it was time Kerry goes out and does what is best for him and his family and get a huge multiyear deal, if possible," Hendry said. "This is really the right thing to do. We've had some really honest conversations in the last week. We don't have to get into how much I think of him, but at the same time I don't think we could do for him right now what he deserves and what I think he'll get going elsewhere."
Wood made an immediate impact as a rookie when he struck out 20 Houston Astros in his fifth major league start. He had four double-digit win seasons for the Cubs, but his career has been sidetracked by elbow and shoulder injuries.
When it appeared his career might near an end because of shoulder problems, Wood returned to the bullpen in August 2007 and pitched well. He then won the closer's job last spring and finished 2008 with 34 saves in 40 chances, a 3.26 ERA and a 5-4 record.
In 10 seasons with the Cubs -- he missed 1999 after elbow ligament replacement surgery -- Wood compiled a 77-61 record with a 3.65 ERA and 1,407 strikeouts in 276 games. He also made 12 trips to the disabled list during the decade.
Gregg was acquired for minor league pitcher Jose Ceda.
Bothered by a sore left knee, Gregg finished 7-8 with a 3.41 ERA and 29 saves. His nine blown saves tied for most in the majors.
Hendry said Gregg had knee surgery, will begin throwing in January and will be ready for spring training.
"My surgery I had was kind of a maintenance issue," Gregg said in a conference call.
"It definitely hindered my performance in August and limited the amount of pitching I did in September. ... I'm 100 percent confident I'll be 100 percent going into next year."
Gregg had a 10.13 ERA for August, but his ERA was under 2.00 for every other month, including seven scoreless innings in September after he lost the closer job. He had 72 appearances and held batters to a .203 average.
The trade was not a surprise because Gregg is eligible for arbitration. He was the Marlins' highest-paid player in 2008 at $2.5 million.
He is the fourth arbitration-eligible player traded by the Marlins this offseason, joining first baseman Mike Jacobs, who was traded to Kansas City, and outfielder Josh Willingham and starting pitcher Scott Olsen, who were traded to Washington.
Going to the Cubs was a plus, Gregg said.
"It's one of those teams I've always said I'd love to play there and go to Chicago and play for the Cubs. I can't say enough about the atmosphere in Chicago and being there."
Gregg joined the Marlins before the 2007 season in a trade from the Angels and had 32 saves in 74 relief appearances that year. He has an 18-21 career major league record with 62 saves with a 4.00 ERA in 271 games -- all but eight relief.
The right-handed Ceda, who is only 21, was 4-3 with nine saves and a 3.83 ERA last season in minor league stints at Class A Daytona and Double-A Tennessee.
"Jose is a big, strong kid with a real live arm," Marlins GM Larry Beinfest said. "We think he can help us in the back end of our bullpen in the very near future, if not right away."
Information from The Associated Press was used in this report.