Cheney’s office said in a statement on Friday: "The vice -president will represent the United States at the opening session of Afghanistan's new, democratically elected parliament."
He will also meet Hamid Karzai, the Afghan president, and visit US troops.
Cheney will be among other foreign dignitaries attending the landmark session of Afghanistan's first elected parliament since the 1970s.
His visit comes after elections in Iraq on 15 December that were viewed by the White House as another step towards democracy in that country and the region.
He will also visit Pakistan and plans to meet Pervez Musharraf, its president, whom the United States considers a key ally in the fight against terrorism.
"President Bush has asked the vice-president to stop in Pakistan as well to assess ongoing US relief and reconstruction efforts in the wake of October's devastating earthquake," the statement said.
Some top al-Qaida leaders have been captured or killed in Pakistan, and US officials say Osama bin Laden, the group's leader, is hiding around its mountainous border with Afghanistan.
Musharraf recently announced that a senior al-Qaida figure, Abu Hamza Rabia, was killed in a tribal region bordering Afghanistan.
Cheney will meet the leaders of Saudi Arabia, Egypt and Oman to discuss "key issues of mutual concern relating to President Bush's freedom agenda and the war on terror", the statement said.
Egypt recently held parliamentary elections in which the party of Hosni Mubarak, the president, won about three-quarters of the seats, but opposition supporters have protested that the elections were rigged.