A cleaner raised the alarm on Wednesday after noticing that a glass display cabinet containing footballing memorabilia at the Hearts ground had been broken into.
The total value of the haul, which included an 18ct gold pocket watch, is estimated to be more than £5,000.
The medals were: a Scottish Football League Championship winners’ medal from the 1896-97 season, won by James Mirk; a Scottish Football League Championship winners’ medal from the 1894-95 season, won by George Scott; a Victory Cup final runners-up medal from 1919, awarded to Bob Mercer, and a Victory medal awarded posthumously to Harry Wattie killed in action during the Battle of the Somme in 1916.
Workers at the stadium noticed a suspicious looking man on Wednesday. The theft is believed to have happened between 8am and 4:30pm.
The man is described as white, 40 to 45 years old, 5ft 9in tall, medium build, short ginger hair, clean-shaven, wearing a dark bomber jacket and dark trousers.