The agreement was reached just before an official ban on prayers in the street is implemented across the country.
In an interview with Le Figaro, interior minister Claude Guéant confirmed the agreement had been signed on Wednesday evening and said he would remain "vigilant without fail" about ending street prayers.
"Praying in the street is not dignified as a religious practice," he said. "It contravenes our principle of secularism."
He said the new mosque would provide "an area of 2,000 square metres" and would be "rented for €30,000 a year."
A former fire station will be used for the mosque, which can receive up to 2,700 people.
On Wednesday, there were signs that the mosque might not be ready for prayers on Friday. Magazine Le Point reported that work was running late. "We are not cattle," it quoted one Imam as saying.
Prayers in the street became a national issue when Front National leader Marine Le Pen provoked outrage by comparing street prayers to the Second World War, likening them to an "occupation."
"There may not be armoured vehicles or soldiers, but it's an occupation all the same and it's hard for the locals," she said in December 2010.
The national ban on prayers in the street comes into force on Friday.