John Black, 35, broke into the Welsh midfielder's £1 million home in Bothwell, South Lanarkshire, before ransacking every room and stealing football tops and baby clothes.
Black, of Hamilton, has already been behind bars for stealing from Mr Strachan, when the then Celtic manager stayed in the same street in the upmarket village.
Black was jailed for two-and-a-half years for that incident and is now facing a further spell behind bars.
Black appeared at Hamilton Sheriff Court and admitted to the raid in Mr Ledley's home in an area dubbed 'millionaire's row' because of the high number of footballers and wealthy residents living there.
Depute fiscal Imran Bashir told the court the incident happened in 2011 after Mr Ledley, 26, had locked up the house and gone out.
He added: "He had locked and secured the premises but the alarm was not on due to technical problems with it.
"He left and on the March 5 around 2am the accused with another individual climbed over the rear fence and into the property.
"They forced the living room window open with a screwdriver and gained entry. They went into all the rooms looking for property to steal.
"The accused stole two Celtic football tops with 16 and Ledley on the back, the relevance being that Mr Ledley plays for Celtic FC.
"The accused also stole a baby's Burberry jacket and then they left the property."
A neighbour saw the damage to Mr Ledley's rented home and alerted him to the break-in.
Depute Bashir told the court Black had later been held by police on a different matter and admitted the raid on Mr Ledley's home.
He added: "The accused was detained on another matter and asked to speak to an officer. He then gave detailed knowledge of this offence and was charged. The items stolen were not recovered."
Black's lawyer Kevin McCarron said: "There have been no convictions since this happened nearly three years ago.
"He has made efforts to address personal issues he has and even though I know this could be dealt with today I would ask for reports to be done."
Sheriff David Bickett deferred sentence until January and continued Black's bail.
Mr Ledley moved to Celtic in 2010 after leaving former club Cardiff City and lived in Bothwell with his partner Ruby. The pair have never commented on the theft but have since moved to Glasgow.
Black stole football mementoes and expensive gadgets from Mr Strachan's property in 2008.
His haul included a signed football jersey, a laptop, an electronic games console, a digital camera, a wallet, bank cards, a TV viewing card, a driving licence, a camera, a battery charger, a webcam, an iPod, a rucksack, video tapes and a pair of shoes.
A day after the housebreaking, Mr Strachan referred to the theft as he collected a manager of the month award.
Asked if he was sleeping well in the tense SPL title run-in with Rangers, Mr Strachan said: "I'm sleeping too well. It will be self explanatory in a wee while, I'm sure, but I'm sleeping too well, trust me.
"You might find out what I'm talking about a wee bit later on."