De Gea is finalising an £18.3 million move from Atletico Madrid this week.
Former United and Brondby keeper Carroll told talkSPORT: "It's a lot of money for a 20-year-old keeper but Sir Alex Ferguson knows what he's doing and I think in the last couple of years he's proved how good he is the in Spanish league.
"He's played a lot of games and even in the European Under-21 Championship and Sir Alex will have been watching him for a quite a while and I'm looking forward to seeing him play in the Premier League."
When Carroll was asked about Edwin van der Sar's departure from the club, he went on to say: "They are huge boots to fill.
"It's disappointing seeing Edwin van der Sar go and this young keeper is coming to the biggest club in the world and he's got a lot of pressure on his shoulders.
"Man United is the sort of club that want to win every competition and the pressure of playing for United is a big thing."