The games will take place at Wembley on 2 June and Leeds United's Elland Road on 7 June respectively.
The England manager said: "We're going into a World Cup where we will play African and Central American opposition, so we get that with the games against Nigeria and Costa Rica, but it's not just about the games we've got in the group but hopefully beyond that as well.
"We want to expose the team to different styles and different experiences."
Ticket details for both matches will be announced by the FA in due course but it is good to see the team playing away from Wembley and giving supporters in the north of England the chance to see them in action ahead of the World Cup.