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."

About 15 students, from the 'Fossil Free QUB' group, have been occupying part of the university's administration building since Friday.
A QUB spokesperson said a review of its investment policy is taking place.
The review will be completed next spring.
The spokesperson added that the university is happy to hold discussions with Fossil Free QUB, but there would be no immediate decision taken on its investment policy outside of the review.
The Green Party Northern Ireland, the Social Democratic and Labour Party (SDLP) Alliance Party, Sinn FÃ©in and People Before Profit have all expressed support for the fossil free campaign.
Belfast city Green Party NI councillor Ross Brown was at the demonstration at Queen's, and called for the university to disinvest in fossil fuels.
"There are investment indexes that exist now that exclude fossil fuels, so there's no stopping Queen's choosing those indexes and taking their money out of fossil fuels."
The Sinn FÃ©in MLA Chris Hazzard also said the university should take action now, rather than waiting for the results of a review.
"Other universities around the world, including Sheffield, have recently done this, so it's time for Queen's to do that too," he said.
Meanwhile, freedom of information requests carried out by the Fossil Free QUB organisation - and seen by the BBC - show that some of Queen's money is subsequently invested in;
However, these types of investments are not unusual, according to a wealth management expert.
Ewan Boyle, director of Johnston Campbell financial advisors, told the BBC that many organisations had diverse portfolios.
"If we look at the top 100 companies in the UK, around 25% of those have a bias towards mining or oil, so avoiding those companies if you are a large investor is virtually impossible" he said.
"Queen's are passing their money to fund managers, who are responsible for investing that money, and their primary objective is to get the best returns they possibly can."
"It's what many pension funds, and many large organisations are doing," Mr Boyle added.
"Mining and oil have been huge growth areas in recent years, so that's where the fund managers are investing to get those returns."
A Queen's spokesperson said that university business was continuing as normal, although a small number of staff in the finance office had been relocated.
Celtic have signed Sweden international right-back Mikael Lustig on a pre-contract agreement.
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A number of politicians have attended the protest calling for Queen's University, Belfast (QUB) to sell shares it holds in fossil fuel firms.