Michael becomes seventh signing of transfer window
Tonge, 31, will add valuable experience to the squad as The Lions look to haul themselves away from the Championship relegation zone.
The former Sheffield United and Stoke City man has made 10 appearance for Leeds this season, including the opening day match here at The Den, but has seen his first-team opportunities at Elland Road limited in a turbulent season for the Yorkshire club in which there have been three managerial changes.
Tonge kicked off his career at Sheffield United, making over 300 appearances at Bramall Lane before moving to join Premier League Stoke City at the start of the 2008/09 season for a fee of around £2m.
During his time at the Britannia Stadium the battling midfielder had successful loan spells with Derby, Preston, Barnsley and Leeds United, joining the latter on a permanent basis in January 2013.
Tonge is expected to be in Millwall's squad for this Saturday's Championship clash with Huddersfield Town, but will not eligible for selection to face his his former club at Elland Road the following week.