Lee Birch was locked up for two years and four months over the burglary at the property in Horsforth.
Leeds Crown Court heard the house is shared by a prison officer and a PCSO.
Birch got into the property through an unlocked back door shortly after 6am on December 18 last year.
The defendant stole a PlayStation, an Xbox controller and keys to a Volkswagen Golf and a Honda Civic.
Birch also stole a West Yorkshire Police radio and a mobile phone which belonged to the PCSO along with his bank cards and cash.
A work jacket belonging the the prison officer with an Her Majesty's Prison Service emblem was also stolen and his lap top computer worth £1,350.
Birch was identified as the culprit when his fingerprint was found on a soundbar speaker in the property.
He was arrested at his then home on Haigh Wood Road, Tinshill.
The mobile phone and prison service jacket were found when the property was searched.
Birch, now of Luxor Avenue, Harehills, pleaded guilty to burglary.
He has 43 previous convictions for 165 offences dating back to when he was a child.
Stephen Welford, mitigating, said Birch committed the offence after returning to taking Class A drugs after splitting up with his partner.