Muslim Khan, a Taliban spokesman, said that Fazlullah would make an announcement about the deal on the radio shortly.
"I can't say what he would say, but there would be good news for people of Swat," Khan said.
The development follows talks between local officials and a group headed by Maulana Sufi Mohammad, Fazlullah's father-in-law and the leader of the Tehrik-e-Nifaz Shariat Muhammadi, regarding the implementation of sharia, or Islamic law, in the area.
'Commitment to peace'
"Things are going well so far. Both sides - the local Taliban as well as the government - are happy with the progress of the talks," Raja Asad Hameed from Pakistan's The Nation newspaper told Al Jazeera.
"The spokesperson from the Tehrik-e-Taliban Pakistan, led by Maulana Fazlullah, have already said that they have given full authority to Sufi Mohammad to go for any decision about the fate of Swat.
"It looks as though he has the mandate of all sides ... and he has expressed his commitment to bring in peace, and at the same time sharia law, to Swat."
The government has already agreed to implement sharia in Malakand district, which contains Swat, in return for a ceasefire deal.
Western powers, as well as many Pakistanis, have been alarmed by the government's offer.
Concerns over deal
They fear that a ceasefire could result in another sanctuary in Pakistan where al-Qaeda and Taliban fighters could move freely.
They also worry that Taliban fighters elsewhere in the region will be encouraged by the government's move.
Al Jazeera's Imran Khan, reporting from Islamabad, said that the details of the deal were still unclear and that the Taliban might want to act as the "enforcers" of sharia in Swat.
"The Taliban were trying to get the government to agree to their key demands - they included the implementation of sharia, the release of all Taliban prisoners," he said.
"But what they also wanted was to control [the implementation of] sharia law within the valley - that would mean a much tougher version of Islamic law than the one Sufi Mohammad had negotiated with the government."
Pro-Taliban fighters last week announced a 10-day truce in the region while the talks were under way.