The 68-year-old Swede has signed a three-year contract with his home nation's rivals, Norway, after also coaching Sweden (2000-2009) and Nigeria (2010).
Perhaps his greatest achievement was his 2011-2016 spell with Iceland which culminated in reaching the Euro 2016 quarter-finals while humiliating traditionally stronger England along the way.
Lagerbäck takes over from Per-Mathias Høgmo, who resigned in mid-November after a series of poor results.
Norway are currently ranked 84th in the world by FIFA.
With three defeats and a single victory against San Marino, the country is in second-last place in its 2018 World Cup qualifying Group C.
"This is obviously a difficult situation," Lagerbäck told reporters about the team's chances of qualifying.
"It will be difficult to win the group but there is still a possibility of finishing second," and having a chance at the play-offs, he added.
The move is likely to prove divisive in Lagerbäck's native Sweden, where there is a fierce sporting rivalry with neighbours Norway, as the Guardian's Swedish football editor Marcus Christenson showed in his reaction to the news.
Nooooooooo! Lars Lagerbäck is the new Norway coach. That's it. The world has officially ended. Lars, how could you? Of all the countries...- Marcus Christenson (@m_christenson) February 1, 2017
Lagerbäck's appointment puts an end to the Norwegian federation's more than two-month quest, after former Manchester United striker Ole Gunnar Solskjær and FC Copenhagen's successful coach Ståle Solbakken both turned down the job.
Lagerbäck had most recently served as adviser to the Swedish team since last summer.