Lindgren is the son of Andreas Lindgren and Helga Björk. He studied in Umeå to become a teacher and worked as a teacher until the middle of the 1970s. He was for several years active as a local politician for the Swedish Social Democratic Party. In the 1980s he converted to the Catholic faith.
Lindgren began as a poet in 1965 but had to wait until 1982 for his breakthrough, with The Way of a Serpent (Swedish: Ormens väg på hälleberget). Lindgren has been translated into more than thirty languages and is one of Sweden's most internationally successful contemporary writers. He became a member of the Swedish Academy in 1991.