During a club career that spanned between 1994 and 2010, he represented Högaborg, Malmö FF, Djurgården, Assyriska, Sylvia, Landskrona BoIS, Sichuan Guancheng and Stabæk IF.

Nannskog started up at Högaborg, a small football club from his home city Helsingborg in Scania, the southernmost of Sweden, as a young boy.

He followed Landskrona up to Allsvenskan and did very well, becoming the club's top scorer with 11 goals, playing an important part in them finishing just above relegation play-off.

Together with BoIS' other forward, Danijel Milovanović, both of them became a feared top-duo that led their recently promoted club to the top position of Allsvenskan at the break for the World Cup in Japan and South Korea.

Nannskog left Landskrona BoIS in summer of 2003 to join the Chinese club Sichuan Guancheng on a two-year deal.

He went on to stay for a year-and a half, but terminated his contract in order to play for his old coach Janne Jönsson at Stabæk in the 2005 season.

The Norwegian media felt it was time the Sweden national team took a look at him again with a possible inclusion in the Euro 2008 squad, following his winning goal against Rosenborg on 4 May.

On 24 September, Nannskog scored two goals and made one assist in the semifinal of the Norwegian Cup, helping Stabæk to a 3–0 victory over Molde.

In January 2009 Nannskog was called up to the Swedish squad to face the United States and Mexico during their annual North-American tour.

Nannskog was born in Helsingborg, Sweden to a Swedish mother and an Afro American father (now living in the U.S.), who worked as a basketball coach, jazz singer and ship builder.

Nannskog went on to work at Norwegian television channel TV2 following his retirement, but has since made the move to a similar role at the Swedish national public TV broadcaster SVT.