The 27-year-old will spend the rest of the season in Turkey after dropping out of the first-team picture under Harry Redknapp.
Among his team-mates at Bursaspor will be former England goalkeeper Scott Carson and on-loan Stoke midfielder Maurice Edu.
Ferdinand's last Premier League appearance was on Boxing Day, and Redknapp has sanctioned a move despite Ryan Nelsen's imminent departure for the MLS.
Tal Ben Haim was signed as cover early in the transfer window and South Korea left-back Yun Suk-young will join if his work permit hearing is successful.
But possible moves for West Brom's Jonas Olsson and Brede Hangeland of Fulham are, by the Rangers manager's own admission, all-but dead in the water.