Manager Noel Hunt had said following Saturday's 2-1 victory over Wigan Athletic that a midfield addition would be prioritised as Michael Craig suffered a season-ending injury.
An England Under-21 regular a decade ago, Carroll starred for Exeter City last year and was in League One with Ipswich Town before then, spending the previous decade exclusively in the Championship and Premier League.
Moving to League Two MK Dons last summer, he made 16 appearances but mutually ended his contract last month, leaving him now a free agent heading into the final couple of months of the season.
An experienced operator who could play in any of the midfield areas, Carroll will allow the likes of Wing and Savage a well-earned rest.
Hunt said, "We're delighted to bring in a player of Tom's experience into the building to bolster our options in the final stages of the season.
He's someone who has played a huge number of games across the EFL and Premier League, and as a person he is just the kind of character we are looking to recruit into our squad."