Ms Robison said the move would provide “greater transparency and accountability” following a financial crisis at NHS Tayside.
It was revealed earlier this year the health board had used endowment funding to cover general running costs.
Ms Robison reassured MSPs that returns submitted by other boards had revealed no cause for concern.
The Tories used a debate at Holyrood today to call for the government to publish full details of NHS boards’ finances and provide regular updates.
The party’s health spokesman Miles Briggs warned there were also “growing concerns” about the financial accountability and reporting of the joint boards overseeing the integration of health and social care in Scotland.
Ms Robison said she had agreed to review the progress of the integration authorities and had committed to publishing a medium-term financial framework for the health service in coming weeks.
Monthly information on NHS boards’ financial performance for 2018/19 would also be available from June, she said.
“I hope that Miles Briggs and others agree that what has been set out is a reasonable proposal to address the concerns set out in the motion and provide greater transparency and accountability to this Parliament,” she said.
On the misuse of endowment funds, Ms Robison said returns submitted by all boards had been passed to the Office of the Scottish Charities Regulator (OSCR) for review.
“I can confirm today that there was nothing in the responses that is a cause for concern and no boards are showing retrospective use of endowment funds in order to improve their financial position as happened in Tayside,” she added.
Mr Briggs said: “I welcome the government’s acceptance that we need greater financial accountability of the integration joint boards, but I also believe that we need to now take time to ensure that they are truly fit for purpose.
“We want to see the cabinet secretary commit to a review of the integration joint boards to fully understand their current financial position, but also to look to how effective they have been and what future reforms may be needed.
“We cannot and we will not just stand in the sidelines and watch a crisis in our social care system build ever greater.”
Mr Briggs said he had not called for Ms Robison to resign as the debate was “too important” to be made personal, adding: “The truth is I don’t believe there is anyone on the SNP benches, who could actually step up to the challenge.”
However, Scottish Labour and the Scottish Liberal Democrats renewed their calls for the Health Secretary to resign.
Labour’s Anas Sarwar said she had presided over a “series of failings” and accused the Tories of offering her a “fig leaf for her failings”.
“It appears there are only two people in the chamber who don’t think Shona Robison should go – Nicola Sturgeon and Miles Briggs,” he said.
“Scotland’s NHS needs change, change that starts right at the top of the organisation.”
Lib Dem MSP Alex Cole-Hamilton said: “There are light bulbs flashing all over the dashboard of our NHS in warning of the many problems it faces.”