News of Gregg's pending signing was first reported by Ken Rosenthal of FOX Sports.
Gregg was the Marlins' closer in 2007-08, collecting 61 saves in 74 opportunities.
With the Cubs in 2013, Gregg saved 33 out of 38 games. The right-hander has 177 career saves.
The Marlins have been in the market for experienced relief help.
The bullpen is thin on experience, especially after Carter Capps was placed on the 15-day disabled list with a right elbow sprain. Capps will be evaluated by Dr. James Andrews on Wednesday, and Tommy John surgery is a possibility.
On Sunday, the Marlins dealt a Competitive Balance A Round pick (No. 39 overall) to the Pirates for reliever Bryan Morris, who joined the team on Monday.
The slot value for the No. 39 pick is worth $1.4 million, and that salary space is going toward signing Gregg, who broke in with the Angels in 2003.
Gregg provides another option to set up closer Steve Cishek.
Once the deal is official, Gregg will report to the Marlins complex in Jupiter, Fla., where he will spend about a week getting ready to join the team.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter