Lagerback, who coached his native Sweden for nine years, was picked ahead of fellow Swede Sven Goran Eriksson, Englishman Glen Hoddle, Serb Ratomir Djukovic and Frenchman Bruno Metsu.
He will be assisted by Austin Eguavoen, Daniel Amokachi and Alloy Agu as Nigerian assistants.
The Swede was the last of the five candidates to arrive Abuja and was interviewed on Friday afternoon.
NFF official Tunde Aderibigbe told KickOffNigeria.com that Lagerback both surprised and impressed the NFF's selection panel not only with his deep understanding of Nigerian football and its problems, but also with the solutions he provided to tackle the issues.
"He broke down and analysed the Nigerian team, and analysed the players from as far back as 2002 when Sweden met Nigeria at the World Cup, to the current team and players.
"He went on to identify the problems with Nigerian football and set out specific ideas for solving the problems,
"And then he set specific targets and timelines to meet those targets. His presentation was brilliant and showed that he came prepared.
"The panel were surprised at his knowledge and impressed at his delivery."
The executive committee of the Nigeria Football Association subsequently went into an eight-hour meeting before announcing Lagerback as the new coach.
Lagerback started his international coaching career at cadet level with the Swedish football Association in 1990, before taking over the B national team in 1996.
In 1998, he was picked as assistant coach for the A team by Tommy Soderberg and promoted to co-coach in 2000. In 2004, he was given full responsibility when Soderberg left to manage the Under 21 team.
During his time, Sweden qualified for an unprecedented five major championships.
He resigned as manager in 2009 after Sweden's failure to qualify for the 2010 World Cup in South Africa.