Lanzini, who joined Jazira in 2014, will sign for the club officially when the summer transfer window opens for Dhs49.2m.
The 23-year-old has scored six goals in 22 appearances for the Hammers this season as the club has challenged for a Champions League place.
“I know it’s worth about 12m euros (£9.4m), and you can hardly get a player for that,” West Ham co-chairman David Sullivan was quoted by the Daily Mail as saying.
“We’ve just signed Lanzini on a permanent deal for that sort of money.”
Lanzini struck seven times for Jazira in his debut season after signing from River Plate and was involved in 70% of their goals as they finished runners-up.
However, then manager Abel Braga saw him surplus to requirements as he brought in a new batch of foreign players.
And while Lanzini has shone in the Premier League, Braga has since been sacked and the club struggling in seventh, a whole 25 points adrift of top-placed Al Ahli.
Lanzini is a WHU player for the next 4 seasons, with a further 2 year option.#COYI
— Jack Sullivan (@jsullivanwhu) March 22, 2016