Sarfraz also won the Player of the Match award in the match against Sri Lanka when Pakistan, chasing 237 runs for victory, had slipped from 74 for one to 162 for seven.
After Kohli won the toss and, surprisingly, opted to field first, Pakistan posted an imposing total of 338 for four featuring Fakhar Zaman's maiden one-day worldwide hundred, an innings where he might have been run out for one and was caught off a no-ball on three.
The prime minister further said the Pakistan team had proved itself to be one of the best cricket teams in the world.
"We have got two years until 2019".
That team could find themselves acting as a "path-finder" for the resumption of tours of Pakistan by major cricket nations. These two lads, plus Shadab Khan, are the future of Pakistan cricket and I sincerely hope they will only go in the upward direction from here.
Pakistan welcomed their heroes - the ICC Champions Trophy 2017 winners - as they reached the Lahore International Airport in the wee hours of Tuesday.
He added: "Hopefully this win, everyone will remember, not just for today, not just for tomorrow, but for a very long, long time. We played like we had nothing to lose, now we are champions", said Sarfraz.
Sarfraz was chosen as the captain following his inspirational leadership during the 18-day tournament that was the cornerstone of his team's 180-run victory over India in front of a full house.
Pakistan's first global 50-over title since the 1992 World Cup reflected well on their Australian coach Mickey Arthur, who kept his squad from losing focus after their dismal display against the Indians earlier in the tournament.
Left-arm fast bowler Amir, whose career was nearly ended on the other side of London's River Thames by a ban and jail term he received for his part in a spot-fixing scam during a 2010 Test against England at Lord's, finished with three for 16.
Kohli, himself renowned for rising to the big occasion, admitted India had been outplayed.
"They made us make those mistakes with the way they were bowling, creating that pressure", Kohli told reporters.
"In the end ... you have to accept and admire sometimes the skill of the opposition".