Ten Hag will move to Old Trafford from Ajax Amsterdam at the end of the season after signing an initial three-year contract.
Ten Hag will take over from interim manager Ralph Rangnick, who has been in charge of Man United since Ole Gunnar Solskjaer was sacked in November.
The Dutchman has been in charge of Ajax simce 2017, winning the Eredivisie twice and reaching the Champions League semi-finals in the 2018/2019 season.
Ten Hag can add another Eredivisie title to his list of honours before leaving as Ajax are four points clear of PSV Eindhoven with five games still to play.
"Very excited the club has made the decision so now we all know," De Gea told United's official website ahead of Saturday's trip to Arsenal.
"We know what he has done for Ajax, he has nearly been in a Champions League final, he won titles and he develops players, so I’m very excited.
"I think he plays very good football. Now we have to be very focused on the last games but we are excited to know who is coming. But now let's focus on Arsenal and fight until the end to be in the top four.
"It's good to know and for sure he is already watching the games and thinking about what he can do to improve the team, so that's very good for us. I'm looking forward to working under him.
"Of course, now the focus on Arsenal, it's a final [for us], we have to take the three points, [otherwise] the top four is done. Let's be focused and win the game."
