Barclays is set to relocate to new premises in the town centre.
The two branches, on Queen Street and Church Street, will close in May and a new branch will be opened on Queen Street in former Wallis building.
The building on Church Street has been a bank since 1796 when it was Beckitt, Birks and Co Bankers.
It later became Wakefield and Barnsley Union Bank in 1849 and operated from that branch for 60 years before becoming Birmingham District Counties Banking Co Ltd in 1906 which eventually amalgamated with Barclays Bank Ltd in 1916.
Gerald Alliott, 84, of Colster Close, Gawber, worked at Barclays from 1945 when he was 16.
He worked there for two years before he was called up for service in the Royal Air Force.
He earned just one pound and 15 shillings per week, which is the equivalent of £1.75.
"The buildings on Church Street are some of the oldest in Barnsley. In those days when I was 16, I could go to the post office carrying £5,000 or even £10,000. You won't find that now."
Gerald, who has even written a short history of the bank, said missionary James Hudson Taylor also worked at the bank as a junior clerk before he went to China where he founded the China Inland Mission.
The building on Church Street has been a bank for so long there is a plaque detailing the banking history.
A spokesman for Barclays said the two existing branches would close on May 3 and reopen in the new premises on May 7, during which time all services would be transferred.
She added: " We have been looking for new premises for a while because the two branches are not really suitable for us to expand. It will mean everyone can have access to a full service under one roof."
Customers have been informed of the changes.