The 21-year-old, who is set to join the club when the transfer window opens in the close season, is believed to have cost a record-breaking fee for Brighton of £30 million ($38 million).
Pedro, who made his senior debut in 2019 for Brazilian side Fluminense, joined Watford in 2020 and has scored 24 goals in 80 appearances.
He has been a long-term target for Brighton, with technical director David Weir hailing him as a "brilliant young talent" who will complement their existing forward line.
The signing is a statement of intent from Brighton, who are currently sixth in the Premier League standings and on the verge of qualifying for European football for the first time in their history.
Pedro's arrival will add further firepower to a team that has already impressed this season with their attacking style of play.
Brighton fans will be eagerly anticipating Pedro's arrival, and the Brazilian striker will be looking to hit the ground running and make an immediate impact in the Premier League.