The 24-year-old who is classed as an attacking right-back, can also play in central defence, was out of contract with the Trondheim side.
Lustig, who will link up with international team-mate Daniel Majstorovic, is not eligible to play for Celtic in the Europa League having featured for the Norwegian side in their play-off defeat to AEK Larnaca FC.
The Swedish defender was delighted to sign on at Celtic Park, he said: “This is a really exciting time for me and I am delighted to be committing my future to Celtic.
“I know a lot about Celtic, about the size of the Club, the world-famous supporters and about the quality squad of players which is already there. I´m really looking forward to joining this squad, to the challenges ahead and hopefully playing my part in bringing some success to the Club.”
After securing Lustig’s services, Neil Lennon said: “We are delighted to bring Mikael to Celtic. We believe he has the qualities to make a real impact at the Club and we look forward to him joining us in January.
“He is a player with international pedigree and a defender with great versatility. He is someone who I feel will be a very positive addition to the squad.
“I like his attributes and he can play both positions (right-back and centre-half), but he´s predominantly a right-back.”
Lustig has won 23 caps for Sweden and plays alongside new Celtic team mate Daniel Majstorovic. Scotland fans would have seen the defender play in the 3-0 defeat to Sweden in August 2010, being replaced at half time by Sebastian Larsson.