The 25-year-old, who made more than 250 appearances in six years with the Cards, has agreed a two-year contract.
Yates said: “I rate Joe as one of the best defenders in non-league football.
“He also has a real hunger to test himself at as high a level as he can. He could have stayed at Woking but when I spoke to him his desire to play in the Football League came across very strongly.
“He is a winner. He will put his body on the line for the club and he is going to be handy for us in the opposition’s box because of his set-piece threat.”
McNerney follows hot on the heels of midfielder Simon Walton, who joined from Stevenage on Thursday.