The 28-year-old has penned a one-year contract at Edgar Street, being able to link up with the Bulls outside of the transfer window as he was a free agent.
Jackson started his career with Derby County, making well over 100 appearances for the Rams before heading to Kenilworth Road in the summer of 2007.
He made 37 appearances for the Hatters, but left the club at the end of last season, following the club's financial problems and relegation to League Two.
Jackson will join former Town colleague Stephen O'Leary with the Bulls, with the midfielder having marked his United debut with a goal in the 2-0 victory over Crewe Alexandra last weekend.