The former Sheffield United boss coached Ramsdale last season at Bramall Lane but lost his job in March, while the goalkeeper left in the summer.
Arsenal manager Mikel Arteta signed Ramsdale for £24million and looked set to be an understudy for Bernd Leno.
The 23-year-old shot-stopper, though, has been revelation for the north London outfit and played an important role in the club's 10-game unbeaten run.
He has established himself as the Arsenal's number one, keeping six clean sheets in nine appearances.
And Wilder acknowledged Ramsdale's desire and professionalism to make every opportunity that was presented to him count.
He told talkSPORT Breakfast: "Brilliant. Fabulous. I am delighted for Aaron [Ramsdale], he's a great guy. It was a tough period for him, as it was for everybody.
"We had a few young players there at Sheffield United. There are no hiding places in there especially when you're not getting results.
"I just think it shows you what his character is about. I talked to Steve Round about Aaron when potentially he was moving and I am delighted for the boy
"You've seen the connection he has with the supporters.
"And in the England squad, it opened up a little bit for him in the summer, with a couple of injuries - with Dean Henderson being injured and Nick Pope. he took his chance incredibly well and impressed everybody.
"He has continued to go from strength to strength, so I am delighted for him."