Gilani, a former top aide of Benazir Bhutto, the assasinated opposition leader, will lead a coalition that won last month's general elections, trouncing loyalists of Pervez Musharraf, the Pakistani president.
Terrorism 'first priority'
Terrorism is the biggest threat undermining Pakistan's stability, Gilani told parliament after his win.
"Our first priority will be restoration of law and order and elimination of terrorism from the country," he said.
"Unfortunately some people have made violence a means to express their views. I appeal to all those people to abandon the path of violence and join us in the journey of democracy."
Gilani urged fighters to renounce violence and offered to hold talks with those who give up arms and join the new democratic era.
He pledged political and economic changes in tribal areas as part of a government strategy to fight terrorism and extremism.
"We are ready to talk to all those people who give up arms and are ready to embrace peace," Gilani said.
Pakistan has been a key ally of the United States in its fight against al-Qaeda and the Taliban since the September 11, 2001, attacks on the US.