A vesting 2015 option would convert the deal to a guaranteed third season if Adams appears in 120 games or more over the first two seasons with at least 60 appearances in 2014.
The 34-year-old right-hander is recovering from surgery to correct Thoracic Outlet Syndrome, but is expected to make a full recovery and be ready for spring training.
Adams, who is represented by Seth and Sam Levinson of Aces Inc., chose the Phillies over a group of teams that included the Nationals, Rangers, Brewers, White Sox, Angels and Cubs.
One of the Phillies' top priorities heading into the offseason was acquiring a proven set-up man to handle the eighth inning in front of closer Jonathan Papelbon. They lost 16 games last season that they led in the seventh inning or later.
By contrast, the Nationals and Braves, who finished ahead of them in the NL East, lost 10 such games combined.
Adams leads all set-up men in baseball in holds over the last three seasons with 97. And his 2.06 ERA in that period is second to Atlanta's Eric O'Flaherty, among relievers who worked at least 175 innings.