Weeks has spent his entire career with the Brewers after being the No. 2 overall pick in the 2003 draft, hitting .249 with 148 homers, 430 RBI, 684 runs scored and 126 steals in 1,142 games.
The 32-year-old Weeks hit .274 with eight homers and 29 RBI in 121 games last season. He lost the everyday second base job to Scooter Gennett.
"Rickie is a talented player who will be used at multiple positions," said Mariners general manager Jack Zduriencik. "His toughness, right-handed bat and Major League experience are desirable factors for our 2015 ball club. We look forward to Rickie's contributions this season and see him as a very nice fit, complementing the pieces we already have in place."
To make room on the 40-man roster, the Mariners designated pitcher Edgar Olmos for assignment.