In a televised speech, President Juan Manuel Santos said the group had been granted an extra 20 days.
Under a peace agreement signed late last year all weapons had to be surrendered to the UN by Tuesday.
Farc commanders had argued that they could not meet the original deadline because of delays in building special camps to house demobilised fighters.
According to the deal, which was reached after four years of talks in Cuba, about 7,000 fighters in 26 transition zones were to have handed their arms to the UN by 30 May.
"In a joint agreement with the United Nations and the Farc, we have agreed that the arms hand-over will not end tomorrow as had been planned, but instead within 20 days," Mr Santos said on Monday.
"The change in date does not in any way affect the firm decision and clear commitment of the government and the Farc to comply with the accord."
President Santos also said that the time that the rebels would be allowed to stay in the demobilisation camps would be extended to 1 August.
After that, all fighters must start their reintegration process into civil society.
Earlier this month, the first group to complete the disarmament process received certificates from the UN mission at a ceremony in Bogota..
Thousands of rebels have handed over their weapons since the Farc signed the peace agreement.
The deal put an end to more than five decades of conflict.
President Santos was awarded last year's Nobel Peace Prize for his efforts to reach a deal with the Farc.
The Colombian government and the Farc rebel group have agreed to give rebel fighters more time to disarm.