Austria will visit on Wednesday, 2 June with Romania set for Sunday, 6 June.
Venues are yet to be confirmed but neither game will take place at Wembley, which Uefa will be preparing to host matches in the finals.
Gareth Southgate’s side have been drawn against Croatia, Scotland and the Czech Republic in their Euro 2020 group.
The tournament will take place from 11 June to 11 July.