It also cleared the party of wrongdoing in paying office rent to three cultural societies.
Police examined allegations made in two BBC Spotlight programmes aired in 2014. Sinn Féin denied doing anything wrong.
Spotlight could not establish what the societies were or who was behind them.
A BBC spokesperson said: "We stand by our journalism. We believe the investigation was of significant public interest."
The TUV leader Jim Allister, who tabled a series of questions arising out of the programmes, has said confirmation that the commission found the payments were for "admissible expenditure" is "remarkable".
The assembly said it had no comment to make on Mr Allister's press statement.
One of the BBC programmes reported that 36 Sinn Féin MLAs claimed about £700,000 in total through Stormont expenses to pay Research Services Ireland (RSI) over a 10 year period.
However, the programme-makers were not able to find any evidence of research that had been carried out by RSI and one Sinn Féin MLA was reported to have said they had never heard of the company until they saw it on their annual expenses.
Mr Allister asked the Assembly Commission how much of the money had been recovered.
The Assembly Commission, which runs Stormont, is chaired by the speaker and includes MLAs representing the five main parties.
In its reply, the commission said its review "confirmed that payments for research services, as reported in the programme, were made for admissible expenditure up to and including the 2012/13 financial year".
"As such, no recovery has been sought," it added.
"No payments to Research Services Ireland for work undertaken after 31 December 2012 have been made as a result of changes to the system of financial support for members that were introduced by the Independent Financial Review Panel from 1 January 2013."
Asked about the payment of rent to cultural societies, the commission said its review confirmed the money was for "admissible expenditure" adding that "as such, no recovery has been sought".
Mr Allister also asked about the disclosure that former DUP assembly speaker William Hay's Office claimed more than £4,000 for heating oil in one year.
The Assembly Commission said "the judicial process is on-going".
A former Sinn Féin MLA, Davy Hyland, also told Spotlight that a party expenses claim form for mileage, amounting to almost £5,000, was signed without his knowledge.
Mr Hyland does not drive and said he knew nothing about most of the mileage claimed on his behalf.
The commission found the claim had not been processed "and as such no recovery was required".
It added that the PSNI had concluded the matter should not be referred to the Public Prosecution  Service.
Mr Allister called the Assembly Commission's findings "bizarre".
He said: "The Assembly Commission has now confirmed that none of the £700,000 claimed by Sinn Féin MLAs and paid to Research Services Ireland has been recovered by the assembly, in spite of the BBC finding that no evidence of research carried out by the company could be produced.
"More bizarre still is confirmation that the assembly did not seek to recover any of the rent paid by Sinn Féin MLAs to what the BBC found to be non-existent 'cultural societies' because a review of the Spotlight allegations 'confirmed that payments for rent, as reported in the programme, were made for admissible expenditure. As such, no recovery has been sought'.
"It is remarkable that the assembly would take such an attitude with tax payers' money without explaining how they reached the view that the expenditure was 'admissible'."
Sinn Féin MLAs who claimed almost £700,000 in expenses for research from a company run by the party's finance managers did nothing wrong, the Assembly Commission has found.