Fiona Hyslop had been accused of "cronyism" after Â£150,000 of public funds were given to DF Concerts.
It emerged that former SNP aide had set up a meeting between Ms Hyslop and the festival organisers.
But Audit Scotland has now concluded there was a "clear rationale for the grant".
It said clear conditions had been attached to the money.
The grant was made to help DF Concerts with operational costs related to the change of venue for the annual music festival.
In a letter to an unnamed MSP, the watchdog said the Scottish government had the legal authority to make the grant.
And it said the decision to award the grant to DF Concerts had been a "legitimate policy decision" for Ms Hyslop, and was consistent with advice she received from Scottish government officials.
There was also budget provision for the grant within the Culture and European Affairs budget for major events and themed years, the letter stated.
It added: "There is evidence that the DF Concerts consultants' costs associated with gaining planning consent incurred in 2014 and 2015 for the 2015 event, together with the increase in venue costs, exceeded the grant Scottish government provided.
"There is also evidence that Scottish government has taken steps to confirm that the money was spent in line with the grant conditions through its review of the final report provided by DF Concerts and related invoices."
But Audit Scotland also said there was a need for "enhanced internal clarity and evidence to support decision-making" when similar decisions were made in the future.
It concluded: "We understand that Scottish government requires flexibility to react promptly to circumstances as they arise, but in our view this needs to be balanced with enhanced internal clarity and evidence to support decision-making.
"The Scottish government has work ongoing in this area."
Opposition politicians had questioned why money was given to the festival, which they said brought in huge profits for its organiser.
They also questioned the involvement of Jennifer Dempsie, a former aide to Alex Salmond, was working on a contract for DF Concerts as a festival project manager at the time of a meeting between Ms Hyslop and DF Concerts.
Ms Dempsie had planned to run as a list MSP for the SNP in the Highlands and Islands constituency in the 2016 elections, but decided not to take forward her nomination.
When she appeared before Holyrood's education and culture committee last year, Ms Hyslop insisted the funding was appropriate, transparent and in line with amounts given to other events.
Ms Hyslop told the committee that festival bosses had "expressed concern" about the "long term future" of the event, due to the seven-figure cost of moving from Balado to Strathallan, and said there was a risk the festival could have moved away from Scotland.
The Scottish government published more than 600 pages of emails and documents related to the grant.
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