Madson saved 32 games in 34 chances last year for NL East champion Philadelphia. CBSSports.com was the first to report the right-hander’s agreement with Cincinnati.
The contract is subject to a written agreement and a physical, according to the person who spoke Tuesday night to The Associated Press on condition of anonymity because the deal had not been finalized.
Madson nearly re-signed with the Phillies, but a $44 million, four-year deal collapsed in November and days later Philadelphia reached a $50 million, four-year contract with closer Jonathan Papelbon.
In 491 career games, including 18 starts, Madson is 47-30 with a 3.59 ERA and 52 saves.
After years of success in a setup role, he took over for an injured Brad Lidge as Philadelphia’s closer last season and went 4-2 with a 2.37 ERA in 62 games. The lanky Madson allowed only two home runs and 16 walks in 60 2-3 innings.
Cincinnati slipped to 79-83 last season, finishing third in the NL Central a year after winning the division. General manager Walt Jocketty has spent much of the offseason retooling his pitching staff, acquiring starter Mat Latos and left-handed reliever Sean Marshall in separate trades that cost the Reds pitchers Edinson Volquez, Travis Wood and several promising prospects.
Madson is coming off a three-year deal with the Phillies that guaranteed him $12 million. He earned $5.1 million last year, including $600,000 in bonuses for games finished.
AP Sports Writers Mike Fitzpatrick and Jay Cohen contributed to this report.