The 61-year-old Swede, who is on a five-month contract with the African country, was interviewed on Friday and named after a meeting of the NFF board early Saturday.
Lagerbäck takes over from Shuaibu Amodu, who was sacked after Nigeria lost 1-0 to Ghana in the Africa Cup of Nations semi-finals last month.
He resigned from the Swedish team after failing to qualify Sweden for the 2010 World Cup in South Africa where Nigeria have been grouped with Argentina, Greece and South Korea.
Lagerbäck began work with the Sweden Football Association in 1990, concentrating on the the country’s junior teams.
In 1996, he took over the Sweden B team and stayed there until 1998 when Tommy Söderberg took him on as assistant coach for Sweden.
In 2000, he was promoted to the position of joint-coach, a responsibility he would share with Söderberg until 2004.
Under his guidance, Sweden qualified for Euro 2000, but lost in the group stages. In 2002, he led Sweden to the World Cup, where they lost to Senegal.
Sweden then qualified for Euro 2004 reaching the quarterfinals where they lost to the Netherlands and two years later Lagerbäck took Sweden to their fourth consecutive championship, the first time in their history.
Under Lagerbäck, Sweden also qualified for Euro 2008 where they were eliminated in the group stage after losing 2-0 to Russia.