Goodwin, who gave Trevor Francis his Blues debut, led the club to two FA Cup semi-finals and promotion to the old Division One in his time in charge, from June 1970 to September 1975.
He had previously been manager of both Scunthorpe United and Brighton.
During his playing career, he was a wing-half for Matt Busby's United, then Leeds before finishing at Scunthorpe.
As one of the Busby Babes, he made his first team breakthrough at Old Trafford following the Munich Air Disaster in 1958.
He played in the first game after Munich, just a fortnight later, when the team-sheet in the programme was famously left blank for the club's FA Cup fifth-round win over Sheffield Wednesday.
And he was in the rebuilt United team all the way to Wembley, where they lost 2-0 to local rivals Bolton Wanderers.
Heywood-born Goodwin also played first-class cricket over two summers, making 11 appearances as a fast bowler for his native Lancashire, in which he took a career-best 5-35 against Middlesex at Lord's in June 1955.
After leaving Birmingham in 1975, Goodwin took up an offer to move to the then burgeoning North American Soccer League, where he had two spells as coach, then club president of the Minnesota Kicks.
He remained in the United States for the rest of his life, and died at home in Gig Harbor, Washington State at the weekend.
Birmingham City will pay tribute at Tuesday night's home game with Bolton Wanderers at St Andrew's. The players will wear black armbands and there will be a minute's applause.
Former Birmingham City manager and Manchester United player Freddie Goodwin has died at the age of 82.