Parliament's move cleared the way for the 65-year-old Khan to set up a coalition government and his first major task will be to avert a brewing economic crisis after his party swept to election victory on July 25.
Khan's party won power on an anti-status quo platform, vowing to fight corruption and lift millions of people out of poverty.
Pakistan has been plagued by boom-and-bust cycles and military coups since independence in 1947, as well as by Islamist militant violence in more recent years.
Khan, a firebrand nationalist, has promised to create millions of jobs and build world-class hospitals and school systems in the mainly-Muslim country of 208 million people.
Among his first challenges will be to decide whether to request an International Monetary Fund (IMF) bailout to ease currency pressures, or seek support from China and risk deepening Pakistan's economic dependence on its neighbour.