The Nigerian becomes the Robins' second Premier League capture this week.
Odemwingie, 34, has agreed a deal until the end of the campaign and goes straight into the side to face Fulham on Saturday.
The 20th-placed Robins can overtake their opponents with a win at Craven Cottage.
Odemwingie, who played for West Bromwich Albion and Cardiff City prior to his move to the Potteries, has appeared just eight times for Stoke in each of the last two campaigns, and his last professional goal came ironically against Fulham, during a 4-1 win in May 2014.
The 62-cap international becomes the Robins' second signing of the week, following the capture of Sunderland right-back Adam Matthews on Monday.
Manager Lee Johnson was forced to send midfielder Ben Gladwin back to Queens Park Rangers at the start of the month, and could be looking to add reinforcements in that area, with Brighton & Hove Albion's Andrew Crofts linked with a short-term move to Ashton Gate by the Mirror on Monday.