The Rolf Nevanlinna Prize in mathematical aspects of information science was established by the Executive Committee of the International Mathematical Union IMU in April 1981. It was decided that the prize should consist of a gold medal and a cash prize similar to the ones associated with the Fields Medal and that one prize should be given at each International Congress of Mathematicians.

One year later, in April 1982, the IMU acepted the offer by the University of Helsinki to finance the prize. The prize was named the Rolf Nevanlinna Prize in honor of Rolf Nevanlinna (1895-1980), who had been Rector of the University of Helsinki and President of the IMU and who in the 1950s had taken the initiative to the computer organization at Finnish universities.

On its obverse side, the medal represents Nevanlinna and bears the text "Rolf Nevanlinna Prize". In addition, there is in very small characters "RH 83". RH refers to the Finnish sculptor Raimo Heino (1932-95) who designed the medal, and 83 to the year 1983 when the first medal was minted. On the reverse side, the two figures are related to the University of Helsinki. On the University's seal in the lower right, the text "Universitas Helsingiensis" is readable. The seal is from the 17th century, except for the Cross of Liberty which was added to it in 1940. In the upper left part, the word "Helsinki" is in coded form. The name of the prize winner is engraved on the rim of the medal.