Gårda In 1937, Gren started playing for
Gårda BK. He made his
Allsvenskan debut on 1 May 1938 against
Malmö FF, which resulted in a scoreless draw. During his time there, he played a total of 54 matches, scoring 16 goals.
IFK Göteborg In 1941, he was recruited by IFK Gothenburg. During his time in the club, Gren won one national championships in the 1941/42 season and was top scorer in 1947. He won the first ever
Guldbollen in 1946. His first league match for IFK was in August 1941, when Gothenburg played against Gårda, winning 6–1 with Gren scoring the first goal. His last league game for Gothenburg was on 6 June 1949 versus
Norrköping at
Gamla Ullevi in which Gothenburg lost 1–0. He had played 164 matches for Gothenburg and scored 78 goals.
AC Milan On 11 September 1949, he debuted for
A.C. Milan against Sampdoria, with Milan winning 3–1. During his time with Milan, he became the 'Gre' part of the famous
Gre-No-Li trio with his Swedish teammates
Gunnar Nordahl ('No') and
Nils Liedholm ('Li'). He also earned the nickname the "Il Professore" which is Italian for "the professor". While at A.C. Milan, he won the league title for the 1950–51 season. He made 133 appearances in Serie A and scored 38 goals. Gren also managed Milan in 1952, before moving to
Fiorentina.
Later career In 1953, Gren moved to
Fiorentina, where he made 55 appearances and scored five goals. Then in 1955, Gren moved to
Genoa where he made 29 appearances and two goals. ==International career==