The 15-year-old goalkeeper has been in huge demand in recent months and has spent a lot of time in England training with the likes of Manchester United and Arsenal.
But City are reported to have beaten off their rivals to land Haug, who is currently with Sarpsborg.
It is expected he will formally complete his move in July, after he has turned 16.
"I can confirm that Kjetil will be going to Manchester City next summer," his father and advisor Cato Haug told Norwegian newspaper Dagbladet.
Haug has been likened to Scandinavian goalkeeping legend Peter Schmeichel and he admits he is flattered by the comparison.
"It's strange to be compared with someone that is among the best-ever goalkeepers, and is also one of my role models," Haug said.