The Spaniard overcame a shaky start to his career at Old Trafford and has emerged as one of the best goalkeepers in the Premier League.
De Gea played his part in helping United advance to the UEFA Champions League quarter-finals, pulling off a superb double save as he kept a clean sheet in Wednesday's 3-0 win over Olympiakos, as United progressed 3-2 on aggregate.
Moyes paid a glowing tribute to the 23-year-old, and believes he can still develop further.
"David de Gea has been terrific," Moyes said. "He has been great. He came in as a good young goalkeeper and he is turning into a great goalkeeper with a lot more to come."
De Gea, who has two years remaining on his current deal, has been linked with a summer move to Barcelona, but Moyes appears determined to hang onto one of his key men.
"The club are always going to keep their best players," Moyes added.
"The club will always look to keep the players who they feel they need to."
Meanwhile, De Gea is looking forward to the challenge of keeping Bayern Munich at bay when United take on the reigning European champions in the last eight of the Champions League.
"You've got to be honest and say we haven't been too fortunate in the draw," De Gea told United Uncovered.
"I suppose everyone would agree that they probably are the strongest outfit left in the tournament.
"You're going to get a tough team at this stage, but the main thing is that we go there with confidence now.
"We must fight really, really hard and really go for it. That's what we've got to do. One team's got to win."
Among Bayern's stellar squad are two players De Gea knows well - his international team-mates Javi Martinez and Thiago Alcantara.
"It will be great to see them both here and in Germany for the away leg," De Gea added.
"I get on really well with Thiago and Javi, we have got a fairly close relationship.
"It will be great to see them but let's hope, as great as they are, that they're not quite on top form when it comes to playing in those two games."