The defender will join the Scottish side when his contract with Norwegian side Rosenborg expires on 1st January 2012.
Lustig will sign a three-year contract with the Scottish giants.
“This is a really exciting time for me and I am delighted to be committing my future to Celtic,” Lustig told the club’s official website.
“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.”