Although the Colts did not reveal financial details of the deal, multiple reports put the amount at $22 million -- all of it guaranteed.
With quarterback Peyton Manning missing the entire 2011 season due to neck problems, the Colts collapsed to a 2-14 record that gave them the top pick in the draft.
Manning and the Colts then parted company, with Manning going to Denver and Indianapolis choosing what the team hopes will be another franchise quarterback.
During his career at Stanford, Luck completed 67 percent of his passes for 9,430 yards and 82 touchdowns. He ran for 957 yards, most ever for a Stanford quarterback.
The Cardinal posted a 31-7 record with Luck as a starter.
Luck signed one day after Robert Griffin III, the second player selected in the draft, signed with the Washington Redskins.