"After tough talks with the interior minister, the union and student organisations obtained the right to demonstrate," Philippe Martinez of the far-left CGT union told a news conference.
He called the U-turn a "victory for the unions and for democracy".
The government had earlier cited security concerns in denying permission for the march scheduled for tomorrow, drawing fire from across the political spectrum.
The march will be the 10th in a wave of protests against the labour reforms that kicked off in March, with many descending into violence, notably in Paris and the western cities of Nantes and Rennes.
The government initially insisted on a stationary demonstration, saying it would be easier to control, but the seven unions and student groups organising the demo dug in their heels for a march.
The two sides finally agreed on a shorter 1.6 kilometre (one-mile) alternative route proposed by the interior ministry.
Last Tuesday's violence saw hundreds of masked protesters and police fighting running street battles.
Police used water cannon to quell rioters who hurled projectiles at them and bashed in storefronts, with 40 people hurt and dozens arrested.
France is already on high alert for security threats during Euro 2016, which has also been blighted by hooliganism.
A Paris police statement had earlier complained of "the heavy demands... On the security forces for several months" and pointed to the need for "reinforcements linked to the hosting of the Euro and the scale of the terrorist threat".
The demonstration went ahead anyway, and nine people died as police suppressed the protest.
The government and unions have blamed each other for recurring violence in the protests against the labour reforms.
While the unions have alleged incompetent and heavy-handed policing, the interior ministry accuses activists of turning a blind eye to attacks on police.
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