The Mamma Mia! hitmakers shot to international fame after winning the annual contest in 1974 with their hit track Waterloo.
The 2013 event will take place in the band's native Sweden in May (13) after the country's entry Loreen was crowned the 2012 champion, and Andersson and Ulvaeus have marked the occasion by writing a special theme song.
We Write The Story will be performed at the contest on 18 May (13) and will be arranged by Swedish Dj/producer Avicii.
The show's executive producer Martin Osterdahl, says, "We are extremely delighted to announce that Benny, Bjorn and Avicii (have composed) a unique piece of music for the 2013 Eurovision Song Contest.
"The idea of an (sic) 'Eurovision Anthem' for Malmo 2013 was there from the beginning of the planning of this year’s contest."
The Abba stars add, "It’s a lot of fun and very inspiring."
The 2013 Eurovision Song Contest takes place in Malmo, Sweden on 18 May (13).