The South of Scotland member had referred herself for scrutiny by Holyrood's corporate body amid wider allegations in a newspaper about her private life.
Her solicitor Aamer Anwar said the matter is "now closed" and she is not being investigated by the Public Standards Commissioner or by Police Scotland.
The investigation centred on the decision to hire a professional photographer to produce work for constituency publications, he said.
"When the photographer withdrew consent to use of photographs and the contract could not be completed, Ms McAlpine refunded the expenses to Parliament out of her own pocket and at her own instigation. There was no cost to the public purse," Mr Anwar said.
"Quite rightly the public places a great emphasis on our MSPs telling the truth and making sure public money is used wisely, which is exactly what Joan McAlpine has done. After the Leveson Inquiry, it is equally incumbent on the press to abide by high standards of probity.
"Joan believes it is a great responsibility and a privilege to represent the people of the South of Scotland, and that is the job she is continuing to get on with doing."
SNP business convener Derek Mackay said: "This is a very welcome decision, which draws a line under the matter. Joan has abided scrupulously by the rules, and that has been confirmed today by the cross-party Scottish Parliament Corporate Body. Joan is a fantastic MSP for the South of Scotland, working extremely hard for her constituents and for Scotland."
Derek Croll, head of financial resources at Holyrood, set out the finding in a letter to Ms McAlpine.
It states: "Your letter of 27 February 2014 invited the corporate body to consider whether any breach of the rules has taken place regarding your use of the reimbursement of members' expenses scheme.
"The Scottish Parliamentary Corporate Body considered a report on the matter at its meeting this morning. I am writing to inform you that, on the basis of the report and annexes presented to the corporate body, the SPCB determined that there was no evidence that a breach of the rules of the scheme has taken place."
Written submissions to the corporate body show she repaid the full amount of £1,750 on October 18, 2012.
Ms McAlpine hired Jane McLachlan for photographic work earlier that year.
The MSP explained: "In common with most members of the Scottish Parliament, I send out press releases, newsletters, annual reports and other publications.
"In early 2012, I decided that I wanted to have a bank of photographs that I could use in connection with those publications."
She negotiated a daily rate with Portrack Photography of £175 for the work, to be carried out over 10 days.
Ms McLachlan completed six assignments, she told the corporate body.
"The working relationship I had with Mrs McLachlan broke down irretrievably in October 2012," she wrote.
"At that point she had completed a substantial amount of the work which had been agreed.
"At this stage she indicated to two members of my office staff that the photographs were not to be used."
Ms McAlpine continued: "Mrs McLachlan gave no indication that she would be refunding all or part of the payment she had received. I therefore decided that as the work for which I had claimed expenses could not be completed, I would repay the sum which had been paid to Portrack Photography under the scheme."