Friðrik was born in Reykjavík, Iceland. A first-time winner of the Icelandic Championship in 1952 and of the Scandinavian Championship a year later, he rapidly became recognised as the strongest Icelandic player of his generation. Friðrik's first result of international note was his shared first with Viktor Korchnoi at Hastings 1955–56.
Friðrik's best result in World Chess Championship competition was in the 1958 Interzonal tournament at Portorož, where he finished equal 5th–6th, automatically earning the grandmaster title and qualifying for the 1959 Candidates Tournament (the last stage to determine the challenger to the World Chess Champion) in 1960. In the event, held at Bled, Zagreb and Belgrade, however, he finished seventh of eight with 10/28. He also played in the following Interzonal (Stockholm 1962) but failed to qualify for the Candidates. Among his best tournament results were joint third in the first Piatigorsky Cup, Los Angeles 1963, with 7½/14 and shared first with Ljubomir Ljubojević at Wijk aan Zee 1976, ahead of Mikhail Tal.
In 1978, he succeeded Max Euwe as President of the international chess governing body FIDE. During he tenure he presided over the 1981 Karpov–Korchnoi World Championship match. Since Korchnoi defected from the Soviet Union in 1976, the Soviets were holding Korchnoi's son, Igor. Olafsson delayed the planned September 19 start date of the match in a bid to get the Soviets to release Victor's son. For this attempt, Olafsson drew the wrath of the Soviets, who then backed the FIDE Vice-President, Florencio Campomanes for Presidency of FIDE. After losing the election in 1982, Olafsson was appointed Secretary to the Icelandic Parliament. Friðrik continued to play occasionally into the 21st century, winning a rapid match against fellow veteran Bent Larsen in 2003 by a score of 5–3.
|This section uses algebraic notation to describe chess moves.|
Friðrik usually played the Sicilian Defence against 1.e4 and the King's Indian Defence and Nimzo-Indian Defence against 1.d4. With White, he usually played the English Opening, but he also played 1.d4, 1.e4 and 1.Nf3 many times.
- "The chess games of Fridrik Olafsson". Chessgames.com. 2010-02-22. Retrieved 2014-01-24.
- "Chess Opening Explorer". Chessgames.com. Retrieved 2014-01-24.
- "Former FIDE President Fridrik Olafsson turns 75 | Chess News". En.chessbase.com. Retrieved 2014-01-24.
- Chess magazine, January 1979 – Interview with David Levy
- The KGB Plays Chess – Yuri Felshtinsky