Ten Hag, who left Ajax in 2022 to join Manchester United, narrowly missed Hato's time at the Amsterdam club, which started in February 2023.
The current Bayer Leverkusen manager discussed the young Dutch defender after Friday night's preseason friendly defeat to Chelsea, whom Hato joined for €44 million earlier this summer.
"I bet he regrets not having me at Ajax, given that they haven't won any titles in recent years," said Ten Hag.
"When I left, he arrived, but he's developed and progressed very well. He was one of the best, perhaps the best player in the Eredivisie. He's so young, but already at a very high level."
'Absolutely convinced'
The 19-year-old Hato will get a chance to prove himself early on with centre-half Levi Colwill out for an extended period of time with a significant knee injury. Ten Hag believes it will not take Hato long to adjust to life in the Premier League
"You always need a bit of time, but he has an excellent mentality, so he can develop very quickly. He has all the elements, all the qualities in his game to show that he can become a very successful player.
"I am absolutely convinced that he will be successful at Chelsea. I congratulate Chelsea."
Chelsea kick off their Premier League campaign this Sunday with an away game at Community Shield winners Crystal Palace.