Madson, who missed the entire 2012 season with the Cincinnati Reds after undergoing major elbow surgery, can make an additional $2.5 million based on the number of days he spends on the active roster and an additional $1 million in games-finished incentives.
Eight months removed from ligament-replacement surgery, there is a good chance that Madson, a 6-foot-6 right-hander from Moreno Valley, will start the 2013 season on the disabled list.
But if he eventually regains his 2011 form, when he went 4-2 with a 2.37 earned run average and 32 saves in 34 chances for the Philadelphia Phillies, Madson could be a low-risk, high-reward investment for a team in dire need of back-of-the-bullpen help
In the last two seasons, the Angels tied for the American League lead and led the league in blown saves, with 22 in 2012 and 25 in 2011.
Madson, whose fastball averaged 94 mph in 2011, gives the Angels another hard-throwing right-hander to go with Ernesto Frieri, Kevin Jepsen and Jordan Walden. Madson struck out 62 and walked 16 in 60 2/3 innings in 2011.
But Madson features a changeup that none of the other three right-handers have mastered, a pitch that helped him limit left-handers to a .198 average in 2011.
Pitchers often struggle in their initial return from Tommy John surgery, but many eventually regain their arm strength and effectiveness.
But the right-hander rebounded in the second half of that season, with a 3.91 ERA and 1.000 WHIP inn 24 games, and he had a 2.80 ERA, 37 saves and a 1.057 WHIP in 66 games for the Texas Rangers last season.