Byram, who can play as a right-back or as a right-winger, has left Championship outfit Leeds for Premier League side West Ham.
Evans has backed the 22-year-old to succeed at the Hammers, and believes that the fans will love him.
“This kid is the real deal,” Evans told talkSPORT about Byram. “He has everything – two great feet, good awareness, a fantastic capacity to work hard.
“I know it sounds cheesy if you are a supporter and not in the game but he has a fantastic lung capacity to put everything into a game.
“He’s a great footballer and joined a great footballer in West Ham United and I am sure big Slaven [Bilic] and the team down there will be delighted with what they have got.”
The Scot added: “Could he just go out and make his debut against Manchester City at the weekend? I don’t think he will, but could he? Absolutely. He would be embraced by the West Ham supporters at the end.”
During his time at Leeds, Byram established himself as one of the best young players in the Championship.
The youngster created 21 chances in 25 Championship appearances for Leeds during the 2013-14 season.
The Englishman scored three goals and created 39 chances in 39 league matches for the Whites during the 2014-15 campaign.
Byram scored three goals and created 24 chances in 22 Championship games for Leeds this season.
The youngster is very talented, and if he gets to play regularly in the coming months, then Premier League followers will get to see his quality.