The 35-year-old midfielder, who had spells at English clubs Stoke City, Preston North End and Derby County and German Bundesliga side VfL Bochum, now plays for his home club Akranes.
He will stand in the Independence Party's western Iceland primary on March 21, where party members vote to rank candidates to fill any seats they win in the April 25 parliamentary election.
The party is hoping to win three seats in the western province and if they meet their target Gudjonsson would have to finish in the top three out of the 11 candidates standing in the primary vote to get one of the parliament's 63 seats.
"I've been set on a career in politics for a long time, but it's only now when I've moved back to Iceland that I have the opportunity to do it," Gudjonsson, who spent 13 years playing abroad before returning home in 2006, told Reuters.
"I have strong backing in my age group, but it remains to be seen how I do among the older voters. I am, however, quite confident," added Gudjonsson, who has 58 caps for Iceland.
Gudjonsson, whose father is English club Crewe Alexandra's manager Gudjon Thordarson, comes from a family of politicians in the town of Akranes.
His aunt Herdis Thordardottir holds an Independence Party seat, while another aunt, Inga Jona Thordardottir, has been prominent in the party's politics for years and is married to former Prime Minister Geir Haarde.
Haarde's government collapsed earlier this year amid public protests over its failure to prevent a financial crisis that smashed the island's economy. A centre-left coalition government is in place in the interim.
"Since my return three years ago I have been involved in various local issues, including schooling and sports," Gudjonsson, who is also general manager at the club he plays for, said.
"With the country in the economic state we are in, I think it's essential that there be a renewal in the political system and that new people with new ideas untarnished by the economic crash are given a chance."
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