Mr Andersson went on the show with his son Ludvig, who described his own battle with drink and drugs
"When you have genes and you are putting as much effort into it as I was, it's possible to drink and get addicted pretty quickly. In addition, if you take a lot of other drugs, as I was doing, the process goes even faster," he said.
ABBA's string of hits in the 1970s and 1980s thrust them into the list of top 10 bestselling bands of all time. But their success came to a painful end with the break up of the band's two couples, with Mr Andersson divorcing Anni-Frid Lyngstad and Björn Ulvaeus, his songwriting partner, divorcing Agnetha Fältskog.
"We will never appear on stage again", Mr Ulvaeus told the Sunday Telegraph in a 1983 interview, six months after their last performance in December 1982. "There is simply no motivation to regroup. Money is not a factor and we would like people to remember us as we were: young, exuberant, full of energy and ambition."
Mr Ulvaeus and Mr Andersson have continued to work together, however, writing the music for the musical Chess, composing occasional new songs, and more recently working on Mamma Mia, the hugely successful ABBA musical, which became a hit film starring Meryl Streep and Pierce Brosnan in 2008.
Anni-Frid Lyngstad is now formally titled Her Serene Highness Princess Anni-Frid Synni Reuss of Plauen, after marrying a German Prince. She continues to record and release solo work. Agnetha Fältskog released her last album, My Colouring Book, in 2004 and lives a relatively reclusive life on the Swedish island of Ekerö.
Mr Andersson, meanwhile, continues to perform regularly with the Benny Anderssons Orkester.