Gareth Southgate's squad will meet the Republic ahead of their last two UEFA Nations League Group A2 fixtures away to Belgium on November 15 and home to Iceland on November 18.
New Zealand withdrew from next month's planned fixture earlier this month due to travel and player availability complications caused by the coronavirus pandemic.
It will be the Republic's first trip to Wembley since 2013, when the game finished 1-1 and a first meeting since the goalless draw between the countries in Dublin in June 2015.