The Northern Irish centre-back joined the Baggies from Manchester United for £6million late in the summer transfer window and has been impressive early in his career in the West Midlands.
Albion have kept a pair of clean sheets in Evans' two Premier League starts and former United colleague Fletcher has been over the moon with the form of the defender.
"Jonny is a fantastic signing. I spoke about it when he came and I was so excited when he signed," said the Albion captain.
"He's a top player. A great leader and a good talker and I think it's a fantastic signing for the Albion. He's going to be a mainstay in that defence for a number of years. The clean sheets are no coincidence and there's more to come.
"He's a great lad and I can't speak highly enough of him. I knew we were getting a top, top player.
"One of the best defenders I've ever played with at Manchester United and now here."
Fletcher also revealed that he had some part to play in Evans making the move from Old Trafford to The Hawthorns.
"I was constantly on the phone to him. Probably doing his head in, I was phoning and texting him every day," he added.