The Netherlands international signed from Ajax in a £40million deal last week.
Fletcher, speaking to United's official website, has hailed Van de Beek - and revealed what specifically impresses him.
"He's a top-class player and I think he's a fantastic signing," said the Scot. “For somebody at his age, for that price, I think it's a no-brainer.
“I saw him during Ajax's run to the Champions League semi-finals last season [in 2018/19], he was probably one of the catalysts for that.
“What I like about him is his flexibility in midfield.
“He understands when he needs to be a no.10 and what he has to do and he understands when he has to be a box-to-box midfielder; he's got that Ajax upbringing in him and is a cultured footballer.
“I just think he's a great addition and he seems like a great guy as well, given the way he's been treated since leaving Ajax and how everyone has spoken about him.
“There's nothing better than having players in your team that are top players but good people as well. It definitely goes a long way."
Fletcher also believes Van de Beek gives United more strength in depth, opening up on his own experiences in the process.
“You really need strength in depth in there because you've got a big number of games to play and injuries are going to happen, so you need strength in depth all over the pitch," he added.
“When I was at United we had five, six, seven midfielders fighting for two or three spots.
“And sometimes you got the jersey, you were the man in form and sometimes you were on the outside looking in – that's just the way it is and the way it should be at a top club.
“You should be pushing each other. You shouldn't think that you're an automatic starter, and by adding players like Donny it gives competition for places and that squad depth."