The 18-year-old has scored three goals in 25 league appearances for the Blue Square Bet Premier side and started for the Exiles in May's FA Trophy final defeat at Wembley.
The Wales Under-18 captain, who is on standby for the latest Under-21 team, has signed a two-and-a-half-year deal and will join the npower Championship club's development squad.
Wolves head of development and recruitment Kevin Thelwell told the club's official website: "There has been a lot of interest from Premier League and Championship clubs in Lee. We have been tracking him for a long time.
"For an 18-year-old player it's going to be a good step for him coming into the Elite Stage of the Under-21 league and those games - and the pace and intensity of training - will be different to what he has been used to even though he has been full-time at Newport.
"I very much see the remainder of the season being an induction into the Wolves way and into our style of play and getting him up to speed both mentally and physically and technically and tactically as well."
Evans added: "I had been aware of a few clubs that were looking from reading the local press back home. But as soon as I knew Wolves were interested I just wanted to get here as quickly as I could.
"The facilities are superb here and it is a great opportunity for me.
"I do want to thank everyone at Newport for everything they have done, especially the manager Justin Edinburgh for giving me my chance. For him to have all that faith in me and pick a 17-year-old to play at Wembley was unbelievable."