John Black, 35, broke into the Welsh midfielder's £1 million home in Bothwell, Lanarkshire in March 2011, and ransacked every room.
Black, of Hamilton, has already served a prison term for robbing Scotland boss Gordon Strachan when he stayed in the same street in the upmarket village.
He was jailed for two-and-a-half years for that incident but yesterday was ordered to perform 300 hours of unpaid work for the Ledley robbery.
Ledley, who now plays for Crystal Palace, had left the house just hours before Black broke in, forcing the living room window open with a screwdriver.
He left with two Celtic football strips and baby clothing which have never been recovered.
Yesterday defence lawyer Kevin McCarron told Hamilton Sheriff Court Black had beaten a drug problem and was now a reformed character. He said: "He has been fully co-operative with this case and he made full and frank admissions.
"He was gripped by a heroin addiction and at the time... and he says it was behind the crime.
"He has spent the three years wisely and has been on a number of programmes."
Sheriff David Bicket said: "If you don't carry out the order then it can be revoked and all options would be open to the court, these include custody."