"We have accepted to give up the armed struggle because the government has agreed to the complete enforcement of the sharia laws," Muslim Khan, a Taliban spokesman, told the AFP news agency on Thursday.
"We are happy about the agreement but the success of it depends on the conduct of the government, especially in enforcing the sharia laws."
A senior government official in the North West Frontier Province (NWFP) said an Islamic scholar will assist secular courts to decide on disputes according to Islamic laws.
However, a parallel mainstream judicial system will still function.
"It will be the choice of the complainant whether to go for settlement according to sharia or the Pakistan penal code," the official said.
The 15-point peace deal also says that the fighters had agreed to shut down training camps.
Over the past years dozens of people have been killed in suicide bombings in the area.
Khan denied, though, that there were any training centres to prepare suicide bombers in the district.
He said a committee will decide about the release of about 100 men who were arrested by security forces.
"About an amnesty for Maulana Fazlullah's followers, any decision will be taken later. He has thousands of followers," Khan said.
Negotiations with fighters in Swat were launched when Pakistan's new government came into power in February, after routing the political allies of Pervez Musharraf, the Pakistani president.
In October the Pakistan army launched a major offensive against fighters loyal to Fazlullah after they drove police and paramilitary forces from their posts in Swat.
The pro-Taliban fighters had effectively established their own law in the region.
Fazlullah is the son-in-law of another pro-Taliban figure, Sufi Mohammed, head of the Tehrik Nifaz-e-Sharia Muhammad (Movement for the Enforcement of Islamic Law), who was recently released by the Pakistan government from detention.
Mohammed controls Malakand, which is the gateway to the Swat valley.
Jean-Marie Guehenno, the UN under-secretary general for peacekeeping operations, said on Thursday that the world will closely watch the Pakistan-Taliban deal.
"Certainly any cross-border movement is bad, is dangerous," he said during a visit to Afghanistan.
"We will watch closely the situation in the area concerned and make sure that the situation does not deteriorate on the other side of the border."
Earlier on Wednesday, the US said it will "reserve judgment" on the peace deal and will monitor how effective it is in curbing violence.
"We'll see. We'll reserve judgment on these things," Sean McCormack, a state department spokesman, said.
US, Nato and Afghan officials have criticised previous peace deals in Pakistan, saying that they have led to an increase in suicide attacks on international and Afghan forces across the border in Afghanistan.