The deal, agreed to Jan. 11 and announced Friday, calls for a $6 million salary this year, of which $2 million is deferred until Nov. 1 and $2 million until Nov. 1, 2013. The agreement includes a $11 million mutual option for 2013 with a $2.5 million buyout.
Madson saved 32 games in 34 chances last year for NL East champion Philadelphia. He replaces Francisco Cordero as the Reds' closer.
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.