The Netherlands international has joined United from Ajax on a five-year deal for a fee that could rise to as much as £39.1million (€44m).
The midfielder said last week he already feels at home in England’s north west after his arrival was heralded by fans on social media.
Fletcher, a five-time Premier League winner with United, thinks Ole Gunnar Solskjaer’s first signing of the transfer window could prove to be an outstanding one.
“He’s a top-class player and I think he’s a fantastic signing,” Fletcher told United’s official website. “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".