Born in Bury, Lancashire, England, he started his career with Oldham Athletic and Hibernian, but he is best remembered for playing for Rangers during the 1990s, when he earned the nickname "The Goalie".

[12] He served as club captain for the majority of his stay in the capital, and in 1988 achieved the unusual feat of scoring a goal in a Premier Division match, against Morton, with a long kick.

Having replaced Chris Woods, Goram found himself under scrutiny in his first few months, and was criticised for goals conceded against Hearts and Sparta Prague which some regarded as being "soft".

[17] Goram soon settled at Ibrox and established himself by playing in all 55 of Rangers competitive games and keeping 26 clean sheets during his first season there.

[19] These games included home-and-away wins over Leeds United and an unbeaten run that saw the club narrowly miss out on a place in the final.

[17] Goram underwent knee surgery in the summer of 1993 and missed most of the following season whilst recovering, making ten appearances.

[17] He was placed on the transfer list by manager Walter Smith in the summer of 1994;[10][17][20] however, he was allowed to remain at Rangers when he proved his fitness and commitment during pre-season training, and he returned as first-choice goalkeeper for season 1994–95.

[17] He continued to excel in goal for Rangers, with Celtic manager Tommy Burns lamenting in January 1996, "If anyone gets round to doing my tombstone, it will have to read: Andy Goram Broke My Heart.

[31][32][33][34] A four-game return to Oldham Athletic followed, and he retired at the end of the 2003–04 season after a season-long spell at Elgin City, for whom he played five league games.

[37] In October 1985, Scotland caretaker manager Alex Ferguson named Goram in his squad for a friendly match against East Germany at Hampden Park.

[38] In the run-up to the 1986 FIFA World Cup, Goram played the full 90 minutes in friendly matches against Romania and the Netherlands, keeping clean sheets in both games.

[31] Leighton remained first-choice goalkeeper for Scotland in their qualifying campaigns for Euro 1988 and the 1990 FIFA World Cup, with Goram as his understudy.

Goram played one competitive game during this time: a 1–1 home draw against Yugoslavia in October 1988 during the qualifiers for the 1990 World Cup.

[39][40] The match against Portugal was Goram's last Scotland appearance for almost a year due to his undergoing knee surgery and a lengthy return to fitness.

Craig Brown controversially selected Goram ahead of his counterpart for Scotland's matches in Euro 96, despite the fact that Leighton had played in most of the qualifiers.

[43] Brown then selected Leighton for France 98 which prompted Goram to walk out of the squad completely,[44] fifteen days before Scotland were scheduled to play Brazil in the opening game of the tournament.

[61] A left-handed batsman and right-arm medium-pace bowler, his most significant act was probably to clean bowl England Test player Richard Blakey in a NatWest Trophy game against Yorkshire in 1989.

[66] He was the son of Edinburgh-born Lewis Goram, who had played professionally in goal[65] in the 1940s and 1950s for Leith Athletic, Hibernian, Third Lanark and Bury.

[58] On 29 August 2022, the league game between Hibs and Rangers at Easter Road was preceded by a minute's applause for Goram and his picture was shown on big screens.