Speaking to the media at a reception hosted by Prime Minister Nawaz Sharif for members of the victorious team that won the Champions Trophy in England, Khan said there was no one better to lead the Test side than Sarfraz.
"Sarfraz will be the new Test captain as he has shown the leadership qualities in the Champions Trophy," Khan said.
"I am honoured to be appointed Test captain," Sarfraz said during the ceremony.
"I will do my best to lift the team in all three formats and will not rest on Champions Trophy laurels."
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Misbah remained captain from late 2010 onwards going on to become the most successful Test captain in Pakistan's cricket history.
Sarfraz has now earned the honour of being Pakistan's captain in all three formats of the game.
The diminutive player who is 30 has already appeared in 36 Tests, 75 ODIs and 36 T20 internationals.
Khan said that Pakistan had shown with their performance in the Champions Trophy that they were among the best in the world.
Pakistan easily lost their opening group game against India but made a strong comeback with fast bowler Hasan Ali and opening batsman Fakhar Zaman playing pivotal roles.
Ali took 13 wickets in the tournament and Zaman scored two half centuries and a century in the final. Pakistan went on to beat South Africa and Sri Lanka in the remaining two group matches before humiliating title favourite England in the semifinals.