Mr Varoufakis will bring the ECB before the European Court of Justice to try and force the publication of two documents disclosing the legal arguments for cutting funds to Greek banks in 2015.
Greece was plunged further into economic crisis without the emergency funding from the ECB, which had been keeping its banks afloat.
The ECB has claimed the reasoning behind the decision should remain a confidential matter.
It rejected demands for the documents to be published before the court case was brought.
However lawyers representing Mr Varoufakis claim there is a clear European public interest in knowing how it made the call.
Backed by left-wing German MEP Fabio De Masi, Mr Varoufakis has suggested the decision to limit funds to Greece may have been made on political grounds, not because Greece genuinely did not need the money.
Mr Varoufakis and Mr De Masi say if the decision was made for political reasons, the ECB dramatically overstepped the boundaries of its role.
Mr De Masi said: “By reducing liquidity to the Greek banking sector, to force the government to cut pensions, raise taxes and sell off public companies, the ECB overstepped its mandate.”
Following the ECB’s funding cut, Alexis Tspiras’ government, in which Mr Varoufakis was finance minister, had to shut down banks and impose capital controls.
This weakened Greece’s negotiating position with international leaders during bailout negotiations.
Mr Varoufakis resigned from the government, leaving Mr Tsipras to make a deal that gave Greece cash in return for implementing austerity measures and finance reforms.
The ECB can refuse to provide emergency funding if it “interferes with the objectives and tasks” of the Eurosystem, including maintaining price stability and safeguarding payments.
However the two plaintiffs want to know more about the decision.
Mr Varoufakis and Mr De Masi’s lawyer, Andreas Fischer-Lescano, said: “There is an overriding public interest in knowing how far the ECB weighed different goals against each other and how they themselves and their legal experts have interpreted the legal framework in this respect.”