Sven Mislintat says Carlos Borges “immediately understood” what Ajax could offer after the winger spoke to the Dutch giants.
The Portuguese forward has signed a four-year contract with the Eredivisie side after leaving Manchester City for a fee worth around £17m.
West Ham had been interested in the 19-year-old and were at one point in advanced talks to sign him.
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Brighton, Borussia Dortmund and Eintracht Frankfurt were also tracking the teenager, who is regarded as one of the most talented players in the English youth academy system.
The Hammers are understood to have been put off by the player’s wage demands, allowing Ajax to step in and hijack the deal.
“We had a lot of competition to sign Borges, it was close with other clubs, especially one club from the Premier League,” said sporting director Mislintat.
“But we could enter the race and Borges immediately understood who we are, what we stand for and what’s possible here."
It continues to be a difficult summer for David Moyes in east London despite a British record £105m windfall following the sale of Declan Rice.
The club are yet to make a first-team signing this summer with the Premier League set to return next weekend, having seen offers for the likes of Harry Maguire, Joao Palhinha and James Ward-Prowse rejected.
