Adams, 39, takes over from John Sheridan, who left the League Two club after failing to guide them promotion.
Glasgow-born Adams led Ross County to the Scottish Premiership and to their first Scottish FA Cup final appearance and two Scottish Challenge Cup finals.
As a player he turned out for Aberdeen, Burnley, Ross County, Motherwell, Ayr and Livingston.
Adams said: “This is a big football club. It’s a pleasure to come here and work for Argyle.
“It wants to get back to where it thinks it belongs, and that’s in the Championship. For me, that’s the ambition this football club wants to show.
“That’s why I’m here. I’m here to try to make the football club successful, like John Sheridan did before, to move that on.”
He follows in the footsteps of a number of Scottish manager at Home Park, a list which includes Paul Sturrock, Bobby Williams and Dave Smith.