He died suddenly at the age of 73 on Friday, the Edinburgh side have announced.
In seven years at Tynecastle he completed a clean sweep of domestic honours, famously hitting a brace against Celtic in the 1956 Scottish Cup final.
He began his career at Hibs, and after leaivng Hearts went on to play for West Ham, Scunthorpe and Peterbrough - arriving at the Old Showground in March 1963 from Upton Park.
During his time in North Lincolnshire he netted three times in 38 appearances before heading to London Road, helping the Iron to finish ninth in Division Two (now the Championship) in 1962/63.
Crawford left Scunthorpe in October that same year, a season when the Iron were relegated down to Division Three.
Hearts operation director Campbell Ogilvie told Hearts News: "Winning two league titles, three League Cups and a Scottish Cup, he won every domestic honour with Hearts and was rightly regarded as a legend by the supporters."