The 65-year-old, who caused a storm when he no-balled Sri Lanka star Muttiah Muralitharan for an illegal bowling action in 1995, took Aus$9,005.75 (US$7,041) between February 25 and April 28 this year.
The Sydney Morning Herald said Hair had a gambling problem and that he was fired when his bosses found CCTV footage showing him with his hand in the till.
Hair, who stood in 78 Tests from 1992 to 2008, pleaded guilty to one charge of embezzlement and one of stealing on Monday, documents from the Orange Local Court showed.
"This is an aberration in the life of a man who, prior to this, had a lifetime of service to the community and to a sport that he loved."
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Magistrate Michael Allen did not record a conviction but sentenced Hair to an 18-month good behaviour bond, noting that he repaid the money.
Hair caused an international row in 1995 when he repeatedly no-balled Muralitharan for throwing, which is illegal for cricket bowlers. He later said many match officials shared the same doubts but that some were scared to intervene.
Hair was also one of the umpires in 2006 when Pakistan become the first side in history to forfeit a Test after being penalised five runs for alleged ball-tampering against England.