His first public remarks, made in a televised statement, came 17 hours after his main rival, former prime minister Nawaz Sharif, declared victory.
Khan had vowed that the polls would sweep his Pakistan Tehreek-e-Insaf party into power.
“I congratulate the entire nation for taking part in such a massive democratic process. We are moving forward on the path of democracy,” the former cricket star said, speaking from the hospital bed where he is laid up with a fractured spine.
Khan, who fell from a hoist raising him to the stage at an election rally in Lahore last Tuesday, electrified much of the campaign with his calls for reform and galvanised many young people to take part for the first time.
“Even those people who never voted in their life came out and the entire nation is happy to see it. Now there is awareness among the people of Pakistan that their fate is in their hands,” he said.
Sharif’s centre-right Pakistan Muslim League-N (PML-N) is well ahead with more than 115 of the legislature’s 272 directly elected seats, according to various projections by private channels.
Khan’s PTI is projected to win more than 30 seats and become the second largest party in the new assembly, a remarkable achievement given that it only won one seat previously, in 2002.
In reference to allegations of vote-rigging made by members of his party, Khan said: “God willing, we will issue a white paper”.
But while PTI’s showing was far short of the victory for which he campaigned, he spoke of satisfaction about the participation of young people and women.
“There is usually victory and defeat, but all the pain of this defeat evaporated after I saw enthusiasm in youth,” he said.
“I also thank our women. Never in the history of Pakistan have women come out and voted in such a big number. It is heartening to see that they have also contributed to efforts to make a new Pakistan,” said Khan.