The two sides have been talking about a deal that would pay Bell $9 million a year. The deal also includes a vesting option for a fourth year.
Bell is expected to take his physical Friday in Florida, the sources said.
But with the future of their incumbent closer, Juan Oviedo (aka, Leo Nunez), a major question because of an identity-discrepancy issue, the Marlins have been quietly aggressive in their pursuit of Bell since the day the free-agent negotiating period began four weeks ago.
The 34-year-old right-hander is coming off a 43-save season with the Padres that made him the only closer in baseball who has saved 40-plus games in each of the past three seasons.
The Padres have remained interested in re-signing Bell to a shorter deal. And clubs in the closer market say the Angels and Blue Jays also had shown interest.
While Bell's strikeout rate declined in 2011, from 11.1 strikeouts per nine innings in 2010 to 7.3 this year, his average fastball velocity (94 mph), WHIP (1.15), ERA (2.44) and opponent average (.223) were all in line with his previous performance.
Senior writer Jayson Stark covers Major League Baseball for ESPN.com.