The 24-year-old defender, who has been with Rosenborg since 2008, will join Celtic in January after signing a three-and-a-half year deal.
Lustig told the Glasgow club's website: "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."
Lustig won his 23rd cap for Sweden in this month's 1-0 friendly defeat by England at Wembley.
We believe he has the qualities to make a real impact at the club and we look forward to him joining us in January
"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," he said.
With Wales international Adam Matthews having moved to Glasgow after leaving Cardiff City in the summer, Celtic already have three first-team right-backs on their books, the others being Scotland cap Mark Wilson and South Korea's Cha Du-Ri.
However, Celtic manager Neil Lennon said Lustig would be a quality addition to his squad.
"We are delighted to bring Mikael to Celtic," he said about a player who can play at full-back or in central defence.
"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."
Celtic have signed Sweden international right-back Mikael Lustig on a pre-contract agreement.