Onana spent five years in the Barca academy at the start of his career and his impressive form for Ajax this season, helping the side into the Champions League quarter-finals, has seen talk of a return arise.
But the Dutch giants moved to secure the goalkeeper's future in Amsterdam on Thursday, as he signed a new three-year contract, much to the delight of his coach.
"In the past two weeks, because of the international period, we were busy with contracts," Ten Hag told a news conference. "It's great news that Onana extended his contract.
"It's great work from Marc. It's also good for Andre himself and a good sign for Ajax."
Sporting director Overmars also renewed his deal with Ajax last week.
Yet while Ajax are excelling in European competition, they trail Eredivisie leaders PSV by five points ahead of their crucial top-of-the-table clash on Sunday.
Ten Hag remains confident, adding: "PSV are a good team, but we are also good. We have it in our own hands. We have to play well and, if we do our jobs, we have a good chance of winning."
PSV boss Mark van Bommel is also looking forward to a possible title decider.
"Of course, Amsterdam is special," he told reporters. "PSV are, just like Feyenoord, a rival of Ajax. Those matches are big.
"You [the media] have been talking about this, maybe even longer. and that's so good about these kind of matches. A lot of talking beforehand. But that's part of the deal."