The Labour councillor, who represents Dalkeith and Danderhall, discovered that these cost tax payers £700,000.
Cllr Curran sought the FOI after hearing about Police Scotland firearms officer, Rhona Malone who won a landmark tribunal exposing victimisation within the force.
He said: “If there is behaviour going on within Police Scotland that is in any way similar to what we heard in that case, then the public absolutely have a right to know and need to be reassured that something is being done about it.
"Behaviour like that cannot be tolerated. It is toxic, unacceptable and should never be covered up by the use of any gagging order.
“If Police Scotland robustly investigate such cases as they claim to, then they should have no problem with scrutiny and no need for NDAs. I do not believe NDAs have any place in a public body such as Police Scotland, unless there are truly exceptional circumstances and even then, scrutiny is needed.
"I have written to both the Chief Constable and the Cabinet Secretary for Justice, appealing that Police Scotland bring this practice to an end.
“Scrutiny and holding decision makers to account plays a fundamental role for the successful functioning of an organisation, and for the efficient delivery of the service. The benefits of public scrutiny should be embraced.”
A Police Scotland spokesperson said: "Compensation is dealt with on a case-by-case basis and with a view to securing best value for the public purse.
"Confidentiality agreements are recommended by the independent the Advisory, Conciliation and Arbitration Service ACAS and used by both claimants' and employers' solicitors to record the agreement reached between parties.
"In line with ACAS's guidance, we never use confidentiality agreements to prevent whistle-blowing and they have been used in relatively few cases in recent years."