Gordon Irvine, of Broxburn, lifted cash from the back of the ATM at the Lochee branch of Santander before depositing it into his own account.
The 33-year-old spent the money on a car and foreign holidays, and gave £250 to a customer before sleeping with her.
He was found guilty after a trial at Dundee Sheriff Court and will be sentenced next month.
Irvine's lawyer described the crime as "the craziest embezzlement you will ever come across", while prosecutors said he was "living a Walter Mitty lifestyle".
The father-of-two paid for trips to New York, Lanzarote and Rio de Janiero in cash - although he could not go on the trip to Brazil because he could not get the time off work.
He paid £6,900 for a car, fitted his flat with a pool table and three 50-inch televisions, and investigators found £41,000 in his bank account when he was caught.
When one female customer complained about a £25 charge on her account, he credited her £250 before asking to come round to her home that night and sleeping with her.
Irvine's accounts were frozen when he was suspended in June 2013. He resigned the following month.
He denied a charge of embezzling £89,340 from the Lochee High Street bank between November 2010 and June 2011, but the jury returned a majority verdict of guilty.
Sheriff Alistair Carmichael remanded Irvine in custody until his sentencing hearing next month.
He said: "You have been found guilty by the jury of a serious charge of embezzling from a bank where you were in a position of trust.
"Given the nature of what you have been convicted of, I'm not sure I can trust you to turn up and as a result you will be remanded in custody meantime."
A Dundee bank manager has been found guilty of embezzling £90,000 from his own branch.