Mikael Lustig will join the Bhoys on the 1st January, and could make his debut the next day according to Celtic's official website.
The 24-year-old has signed a pre-contract agreement which will keep him at the club on a three-and-a-half year deal.
Lustig expressed his happiness and insisted he cannot wait to get started at the club. 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."
Celtic manager Neil Lennon had admitted his interest in singing the defender on Monday, and now the deal is complete the boss added: "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, but he's predominantly a right-back," added Lennon.