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Lord Bassam has referred himself to the standards watchdog and agreed to repay the cost of travel to and from his Brighton home since 2010.
The peer, who also had a £36,366 allowance for staying overnight in London, says he has not been told he has broken any rules.
But he said it would have been "more appropriate" not to claim the money.
Labour said Lord Bassam, who is a member of Jeremy Corbyn's shadow cabinet, would make way once a successor had been elected in January or February.
A spokesman said the peer had already referred himself to the Lords standards commissioner to determine whether he had broken the peers' code of conduct.
After the Mail On Sunday reported Lord Bassam claimed the £6,400 annual cost of travelling to and from his home in Brighton, the former leader of Brighton Council said he would not submit such claims again.
According to the paper, Lord Bassam is one of a small number of front bench peers also entitled to the Lords office holders allowance. This is because of his role as chief whip and because his main home is not in London.
The payment is included in his salary and designed to cover "expenses in staying overnight away from their main or only residence".
In a statement, Lord Bassam said: "With my home outside of London, I have been in receipt of the relevant office holders allowance for the opposition chief whip in the Lords.
"At the same time, in accordance with rules laid down by the House, I have claimed costs for my regular travel to and from Parliament.
"While I have not been advised that any breach of the rules has taken place, waiving the right to such travel claims would perhaps have been a more appropriate response on my part.
"I will not be submitting any further claims in this way, and instead use the office holders allowance to cover those additional costs. I will also discuss with House officials the steps necessary to repay previous travel claims."