Åke Axelsson studied at the Visby School of Woodwork from 1947 to -51 after which he took an internship at a workshop in Munich where he stayed until 1952. In 1952-57 Axelsson studied interior architecture and furniture design at Konstfack University of Arts, Crafts and Design under the architect Carl Axel Acking.
For some years during the 1960’s Axelsson ran an interior architect studio together with architect Erik Karlström. Of their projects the most prolific is the interior for the Örebro Community Center, designed by Erik and Tore Ahlsén. In 1963 Axelsson won second prize in a competition that had the aim of preserving the beech trees of southern Sweden. Axelsson´s entry was the chair S-217 that was put into production by Gärsnäs.
Five years later Axelsson opened his first workshop in Vaxholm, where he made his first collection of furniture that premiered at the craft center Hantverket in Stockholm. During the 1970’s Axelsson worked as a lecturer in furniture design at Konstfack, while also devoting himself to the study of historical – ancient Greek and Egyptian – furniture.
Axelsson has made several large-scale interior commissions including the Swedish Parliament (with architect Peter Celsing, 1971). Other interior projects Axelsson made during the 1980’s are Stockholm School of Economics and the historic Stockholm restaurant Den Gyldene Freden (both in 1989). In the 1990s and 2000s his commissions included Riksdagsbiblioteket (The Parliament Library) (1997), Carl XVI Gustav's jubilee chambers in the Royal Palace (1995–2001) and the Baltic Centre for Contemporary Art at Gateshead in Great Britain (1997–2002). For the later, Axelsson who made his name with wooden furniture, chose steel pipes and perforated aluminum for the chair Baltic. In recent years Axelsson has designed interiors for the Royal Armoury (2010-2017) and Sven Harrys Art Museum (2018).
In 1988 Axelsson founded the furniture company Galleri Stolen together with his daughter Anna. When the longtime partner Gärsnäs turned 100 years old in 1993 they set up a Nordic design competition. Axelsson sent in an anonymous entry, and won. The winning armchair was called Century, made of beech wood with an upholstered seat. Since 2003 Gärsnäs is owned by the Axelsson's family.
Åke Axelsson has been a member of the Royal Swedish Academy of Fine Arts since 1989. In 1996 he was awarded the Prince Eugene Medal and the following year he received the Bruno Mathsson Award and was honored with professor’s title. In 2022, Axelsson was named an honorary doctor by the Linköping University.