The Mariners released Odom on Wednesday.
Odom will remain in the Rays organization after he went unclaimed off waivers Monday, Marc Topkin of the Tampa Bay Times reports.
Odom was designated for assignment by the Rays on Friday, Adam Berry of MLB.com reports.
Odom's contract was selected by the Rays on Saturday, Adam Berry of MLB.com reports.
The Rays reassigned Odom to their minor-league camp Thursday, Adam Berry of MLB.com reports.
Odom signed a minor-league contract with the Rays on Wednesday as a non-roster invitee, Marc Topkin of the Tampa Bay Times reports.
The Mariners declared Odom a free agent Sunday, Chris Hilburn-Trenkle of Baseball America reports.
Odom was outrighted to Triple-A Tacoma on Monday.
Odom is out of the lineup for Monday's game against the Rangers.
Odom will start at catcher and will bat ninth Monday against the Angels.