Mr Osborne is one of several MPs to be investigated
George Osborne has agreed to repay £1,936 after he was found to have breached the rules on expenses.
The shadow chancellor was investigated by Parliament's standards commissioner over his second home allowance after a complaint from a Labour activist.
The report found that the MP had breached the rules but the offence was "unintended and relatively minor".
Mr Osborne acknowledged the breaches but said he had received "flawed" advice and not benefited personally.
Mr Osborne, who said he had already offered to repay the amount, has always maintained that he was not guilty of any impropriety and he said the report had borne this out.
He said he always clearly designated which was his second home - on which expenses could be claimed - and had not switched properties for his personal advantage.
The Standards and Privileges Committee of MPs, which has the power to take action against members on the basis of the watchdog's reports, said he had already repaid £270 of the £1,936 wrongly claimed and would be asked to repay the remaining £1,666.
Mr Osborne was accused of over-claiming nearly £5,000 on mortgage interest payments on his Cheshire home and also of incorrectly claiming expenses for his London home for a period of time.
The MP said he remortgaged his London home to help him purchase the Cheshire property in 2000 and was told by the authorities to continuing claiming against that mortgage until he could change his arrangements without incurring penalties - which he did in 2003.
The report found the advice Mr Osborne received was "flawed" and he had been incorrect to claim against his London property given that some of the mortgage payments related to the Cheshire home, at the time designated as his main property.
It also found he had breached the rules when he increased his mortgage by £25,000 in 2005 to pay both for repairs of the Cheshire property and part of the original cost of the purchase as some of the sums claimed related to a period before he was elected in 2001.
The committee noted that Mr Osborne had been told at the time by the Fees Office that his claims would be within the rules and that he had not personally gained from the claims.
They concluded that the "the breaches of the rules identified... were not major breaches and were not intentional".
"We entirely accept that Mr Osborne derived no significant benefit from them," their report added.
In a statement, Mr Osborne said he was glad the committee "acknowledge any breaches of the rules were not intentional, not major, and did not provide me with any significant financial benefit".
"As the committee appreciate, I always sought to minimise the cost of my expenses to the taxpayer, and followed the advice I was given. The committee has now decided that advice was flawed.
"I understand the damage the expenses crisis has done to Parliament, and the paramount importance of restoring trust in our politics.
"I want to ensure that the claims I have made are entirely beyond reproach."
The BBC's Political Correspondent Iain Watson said the repayment was relatively small in comparison with those made by some other MPs and would not be regarded as politically damaging.
A number of Labour and Tory MPs have been ordered to repay money after investigations of their expenses by the Standards Commissioner John Lyon while some have apologised to Parliament.