The 22-year-old Byram came through the academy at Elland Road and he was the highest appearance maker currently on the books at the club.
He was out of contract at the end of the season and it was looking increasingly likely he would be leaving this month, as the Hammers beat Everton to his signature.
Byram proved to be a hit amongst Leeds fans since breaking through under former manager Neil Warnock in 2012 and he joins the east Londoners for a reported £3.7m.
Evans told talkSPORT Drive: “This kid is the real deal.
“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 football club in West Ham United and I am sure big Slaven [Bilic] and the team down there will be delighted with what they have got.”
Other young members of the Leeds squad have been linked with big-money moves to the Premier League this month.
The nucleus of the team is made up of youngsters brought through the ranks at Thorp Arch – Byram was one of those, alongside Charlie Taylor, Alex Mowatt and Lewis Cook, with more talent making up the bench. The Scot, who replaced Uwe Rosler in October 2015, says he and owner Massimo Cellino intend to keep their star men.
He added: “I think I can give them [Leeds fans] every assurance as much as every head coach or manager can.
“I don't get involved in the financial aspects here and I didn’t at Rotherham United. From my point of view, I know every player in the world, from Ronaldo to Bale, they have a price.
“But what I would say is it would take a lot of diamonds and a lot of gold to take any youngsters from here. It is certainly the intention from the president and myself to build with them.”
Listen above to Steve Evans, as he spoke to Adrian Durham and Micky Quinn on Drive, discussing Byram, the club’s youngsters, managing Leeds, potential signings and more.
Read more at http://talksport.com/football/listen-steve-evans-drive-leeds-united-boss-sam-byram-transfers-his-job-and-more#wcrEpe1u8SZtblw5.99