Ms Wells had asked the Independent Parliamentary Expenses Authority to audit her travel between 2022 and 2025 after she came under fire for claiming taxpayer money for travel to major sporting events by herself and her husband.
She attracted controversy for spending $100,000 to fly to New York with a staffer to promote the government's youth social media ban at the United Nations.
The expenses watchdog found her travel to New York and costs were within the rules for parliamentary travel.
However, it found four trips were outside the rule, with the minister forced to repay $10,116 that includes a 25 per cent penalty loading.
"The publicly available audit found no misconduct or ethical breaches. The audit found, over four years of travel, involving nearly 250 separate trips, I made four mistakes," Ms Wells said in a statement.
"These were four cases where I chose what I thought was the more sensible, cheaper option, but those choices were not allowed according to the rules, which I accept and respect.
"I accept IPEA's assessment and I am sorry for making these honest mistakes."
The four trips that did not meet the requirements were related to family reunion travel provisions that did not meet the rules.
Prime Minister Anthony Albanese moved to restrict family reunion travel entitlements following backlash to the expenses scandal.
Mr Albanese rejected calls for the minister to resign following the audit report's findings.
"She referred herself to it which was appropriate and it was appropriate that she paid back the money," Mr Albanese told reporters on Friday in Melbourne.
"She has done what the rules require. Anika Wells is a very good minister doing extraordinary work."
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