Haaland, 21, will move to the Etihad Stadium this summer and is set to become one of the highest-paid players at the club. Sources told ESPN he will not top midfielder Kevin De Bruyne, on around £375,000-a-week, as their biggest earner.
According to ESPN sources, the player's release clause is €60 million and Haaland is set to sign a five-year deal at the Etihad Stadium.
A club statement read: "Manchester City can confirm we have reached an agreement in principle with Borussia Dortmund for the transfer of striker Erling Haaland to the club on 1st July 2022.
"The transfer remains subject to the club finalising terms with the player."
Dortmund said once the transfer goes through, the club expects a "positive effect on the key earnings figures for the 2022-2023 financial year" in the range of €35-40m.
Haaland joined Dortmund from Red Bull Salzburg in January 2020 and last season scored 41 goals in 41 games. At international level with Norway, he has already scored 15 goals in 17 games after making his debut in 2019. He has scored 36 goals in 34 appearances for club and country this season.
Earlier on Tuesday, Guardiola had hinted that City were closing on a deal to sign the striker.
The deal means Haaland will play for the club his father, Alfie, represented between 2000 and 2003. Sources told ESPN that Alfie Haaland played a key role in negotiations with City while agent, Mino Raiola, was unwell. Raiola, who also represented Paul Pogba and Zlatan Ibrahimovic, died at age 54 last month.
Dortmund have been resigned to losing Haaland for some time after agreeing to a release clause in his contract which became active ahead of this summer's transfer window.
Information from Reuters was included in this report.