The agreement, first reported by the BBC, brings an end to a chaotic 48 hours in Everton's pursuit of attacking reinforcements, during which two separate deals for Richarlison collapsed and a proposed swap involving Iliman Ndiaye fell apart entirely.
Everton had been exploring parallel interest in Balogun and Richarlison, 29, who left Goodison Park for Tottenham in 2022.
Sources indicate the Brazil forward could not agree personal terms on a return to Merseyside, despite Everton tabling an offer worth £35m, leaving David Moyes to press ahead with the Balogun deal instead.
The move was complicated further by Tottenham's parallel pursuit of Ndiaye, 26. Spurs had struck an agreement with Everton on Friday evening for the Senegal winger to move to north London, with Richarlison going the other way as part of a separate transfer.
That deal unravelled once personal terms with Richarlison broke down, opening the door for Manchester City to step in and agree a fee worth up to £65m for Ndiaye instead.
Born in New York and raised in London after moving there as a child, Balogun came through Arsenal's academy before a loan spell in the Championship at Middlesbrough and a prolific season on loan at Reims, where his 21 Ligue 1 goals convinced Monaco to make his move permanent. Balogun, who left boyhood club Arsenal for Monaco in 2023, has scored 31 goals in 91 appearances across all competitions for the Ligue 1 side.
He has also become a key part of the United States setup, netting 12 times in 31 caps, though his summer was overshadowed by a reversed red card for serious foul play against Bosnia-Herzegovina at this year's World Cup.
Everton's reshuffle in attack comes as Moyes looks to add greater firepower before Tuesday's deadline, with the club still working on separate deals for Manchester City winger Jack Grealish and Fulham full-back Kenny Tete as the window draws to a close.