His resignation was announced by the Elysée Palace following weeks of mounting pressure on the Socialist politician.
The move by prosecutors to open a full investigation into the Swiss UBS bank account he allegedly used to hide assets from the tax authorities, made Cahuzac's position untenable and deeply embarrassing for the Socialist government as he was the minister in charge of combating tax avoidance.
Cahuzac, whose ministerial brief had included fighting against tax evasion, had denied any wrongdoing following a report by the Mediapart investigative website that he had an undeclared Swiss bank account until 2010.
Mediapart said he then transferred the money in the account to Singapore.
It said it had a "trace" of a conversation between the minister and one of his former aides in which he allegedly fretted about the UBS account and then said he had "dealt with the matter."
Prosecutors said police experts had concluded that Cahuzac "is the man speaking" on the tape.
They said they had decided to open a formal investigation into money laundering and fraud.
Cahuzac has dismissed reports of offshore accounts as "crazy claims".
In a statement in December he said: "I have never had an account in Switzerland or any other place abroad."
He also denied figuring in the recording reported by Mediapart.
Mediapart claimed that Cahuzac closed the account in 2010 just before becoming head of the finance committee of the National Assembly.
It alleged he made a discreet trip to Geneva to close the account.
The Tribune de Genève reported that French authorities have sought help from Geneva justice officials over the affair.
Cahuzac continues to deny having an account and vows to "devote all his energy" to defending himself.
In a statement he said he submitted his resignation to President Hollande "out of respect for the proper functioning of government".
The minister, who is a civil plaintiff in a judicial probe into French residents suspected of tax fraud, had previously announced sweeping measures to fight tax evasion.
Weekly magazine L'Express on Tuesday evening reported that Cahuzac had been replaced by Bernard Cazaneuve, who was Junior Minister for European Affairs.