Upton Park boss Sam Allardyce will trigger a release clause in the player's contract, allowing the wide-man to move to London.
The Hammers look to have beat off interest from fellow Premier League sides Everton, Swansea City and West Brom for the 23-year-old, who currently plies his trade for Mexican side Monarcas Morelia.
Everton manager Roberto Martinez reportedly came close to signing Montero for Wigan Athletic in January, when he was in charge of the FA Cup winners.
But it seems the Ecuadorian, who has played 27 times for his country, will turn down the Spaniard for a second time in favour of a move to West Ham.
Montero, who has also enjoyed spells with Spanish sides Villarreal, Levante and Real Betis in recent years, impressed Premier League scouts with a man-of-the-match performance against Argentina earlier this month.
The player's agent has said that he is ready to move to England, and his experiences in Europe earlier in his career might help him to adapt to the conditions.
Write for GiveMeSport! Sign-up to the GMS Writing Academy here: http://bit.ly/12evFlH