International mediator Djibril Bassole, Burkina Faso's foreign minister, confirmed a letter of resignation had been submitted.
The resignation paves the way for the coup leaders to step aside and the parliamentary speaker to take over.
Mali has been grappling with a separatist uprising in the north.
It intensified after the coup by army officers on 22 March.
Mr Bassole, who represents the West African regional bloc Ecowas, met Mr Toure in the Malian capital, Bamako.
"We have just received the formal letter of resignation from President Amadou Toumani Toure," he told reporters.
"We will now contact the competent authorities so that the vacancy of the presidency would be established and so that they take the appropriate measures."
Under the agreement, the Malian parliamentary speaker, Dioncounda Traore, will take over as interim president and govern with a transitional administration until elections are held.
Once he has been sworn in, Mr Traore has 40 days to organise this poll, the deal stipulates.
Mr Traore, who has been in Burkina Faso since the coup was launched, said as he left for Bamako: "I am leaving for Mali with my heart full of hope.