The medals belonged to Arthur Murray, who served on HMAS Arunta during the Korean War.
Sadly, Mr Murray died of cancer in 2009 and never saw his medals again.
Bayswater police station officer-in-charge Dave Whitnell said the medals were spotted in a plastic shopping bag on an outside windowsill at the station on Wednesday, April 23.
He said he believed someone’s conscience had got the better of them a couple of days before Anzac Day.
He was able to present the medals to Mr Murray’s grandson Aidan last Thursday.
Aidan (10) wore the medals to an Anzac Day service in Bayswater.