The young striker is reported to have penned a 5-year deal at Vicarage Road.
He is joining Watford from Rochdale AFC in the second tier of English football.
Baah was born in Germany to Ghanaian parents, but was raised in South London and spent four years in Crystal Palace's academy from 2013-17.
He joined Rochdale in 2019 after a brief spell with non-league side Whyteleafe.
The teenager was named EFL Young Player of the Month for January after scoring a stunning brace against Charlton Athletic.