Born in Aberdeen, Leggat started his career at his home town club as a right winger.
He was part of the Aberdeen team that won the Scottish league title in 1954 to 1955 and the 1955 to 1956 Scottish League Cup.
He six goals for the Scottish League XI in five appearances.
He was transferred to Fulham in 1958 for £16,000, where he formed a right flank partnership with England captain Johnny Haynes.
He wound down his career with short spells at Birmingham, Rotherham and Bromsgrove Rovers and was also briefly a coach at Aston Villa.
Leggat held the record for the fastest hat-trick in the English league, having scored three goals in three minutes in a 10–1 win for Fulham against Ipswich Town on 26 December 1963.
This record was broken in May 2015 by Sadio Mane of Southampton.
Leggat was selected in the Scotland squad for the 1958 FIFA World Cup in Sweden, playing in the Scots’ matches against Yugoslavia and Paraguay.
In total he earned 18 full caps between 1956 and 1960.
In 1971 Leggatt emigrated to Canada, where he began a second career as an analyst on soccer telecasts for the CBC at the 1976 Summer Olympics and at the World Cup.
He later became host of TSN’s popular Soccer Saturday program as well as an on-air analyst on its soccer telecasts.
He was inducted into the Canadian Soccer Hall of Fame in 2001 as a ‘builder’.
His son, also named Graham Leggat, was executive director of the San Francisco Film Society from October 2005 until his death in August 2011.
Scottish footballer Graham Leggat died on August 29, 2015 at age 81.