The Tynesiders have agreed an undisclosed fee with Forest for the 24-year-old, who can play in midfield and across the back four.
Perch, who came through Forest's youth academy, will join Newcastle subject to passing a medical.
Forest's chief executive Mark Arthur said: "James has been a marvellous servant for Nottingham Forest.
"He made it clear that the prospect of a move into the Premier League with Newcastle appealed to him and we couldn't stand in his way.
"I would like to thank him for the service he has given us and wish him all the very best with Newcastle."
Source: PA
Source: PA