Heilman and Olson have already been involved in trades this offseason. The Mariners acquired Heilman as part of a three-team, 12-player trade that sent closer J.J. Putz to the Mets in December.
The Cubs picked up Olson in a deal from the Orioles for outfield prospect Felix Pie on Jan. 18.
Cubs general manager Jim Hendry, who was returning from a trip to Italy on Wednesday, couldn't be reached for comment. But one baseball person said Hendry has been an admirer of Heilman's "since he pitched at Notre Dame.''
Olson had been mentioned as a potential trade chip if the Cubs decided to make another run at San Diego's Jake Peavy. The Cubs' deal with Seattle could put an end to speculation about the team trying to acquire Peavy.
Heilman, 30, has a 22-33 record with a 4.24 ERA in six major league seasons. He blew five of eight save chances last season and heard steady boos from the disenchanted fans at Shea Stadium.
"Categorize last season as kind of an aberration. I didn't throw the ball the way I was capable of and didn't have the results I would have liked," said Heilman, a 6-foot-5 right-hander. "I don't think there was one thing that was the sole cause of last year. I think there were a lot of different factors that played into it."
Heilman has made 305 career appearances -- 280 in relief -- but has expressed an interest in moving into a starting role.
Heilman is expected to compete with Sean Marshall for the No. 5 starting spot in the Chicago rotation behind Carlos Zambrano, Ryan Dempster, Rich Harden and Ted Lilly. Chad Gaudin and Jeff Samardzija are other possible candidates to start for manager Lou Piniella.
"All of our reports say his stuff had no drop-off and was still there," Cubs assistant general manager Randy Bush said about Heilman. "It was a case of poor location in a lot of cases. I think it was a case of an environment where it had gotten negative for him in New York."
The 30-year-old Heilman grew up a Cubs fan in Indiana and graduated from Notre Dame. He said he mostly enjoyed his six seasons in New York and acknowledged that going back could be an interesting experience.
"I didn't have any ill feelings toward anyone or anything there in New York. I enjoyed my time there," he said. "The fans treated me pretty well for the most part. They're a fickle crowd. They know what they like and they want to see their team do well. Sometimes they let it be known."
Heilman dutifully attended a weekend fan function at frigid Safeco Field last weekend and talked enthusiastically about getting a fresh start outside New York.
"We were excited to acquire him, and sorry to trade him," Mariners general manager Jack Zduriencik said. "But I felt this was a deal that we couldn't pass up."
Olson, 25, was selected by Baltimore as the 48th overall pick in the 2005 draft.
While Seattle already has six potential starters in Felix Hernandez, Erik Bedard, Brandon Morrow, Jarrod Washburn, Carlos Silva and Ryan Rowland-Smith, Olson is likely to get an opportunity to compete for a spot in the Mariners' rotation this spring.
Zduriencik said he knew Olson from scouting him in college, when Zduriencik was in Milwaukee's front office.
"I hope his mind-set is he comes here wanting to win a spot in the starting rotation," the GM said. "If we were giving Aaron Heilman a chance to be a starter, which I told him we were, now here's Garrett Olson -- he's young, he's left-handed -- why not give a starting opportunity in the same vein?"
To clear room on their major league roster for Cedeno and Olson, the Mariners waived pitcher Randy Messenger. The 27-year-old right-hander appeared in 13 games for Seattle in 2008.
Jerry Crasnick covers Major League Baseball for ESPN.com. Information from The Associated Press was used in this report.