The right-hander passed his physical in the morning, making the deal official after it had been speculated for weeks that he would be leaving the Cardinals for the west coast.
The 31-year-old Morris went 14-10 with a 4.11 ERA for the Cardinals last season, helping the team advance to the National League Championship Series, where St Louis lost to Houston.
He complied a 101-62 record and 3.61 ERA with the Cards in the past nine years, establishing himself as a dependable starter.
"Simply put, Matt Morris is a winner," San Francisco general manager Brian Sabean said.
"Matt will be a perfect complement to the top of the rotation and provide valuable leadership to our younger pitchers."
The Giants eagerly pursued Morris as soon as the 2005 season ended. His contract contains a club option for a fourth season.