Bishop Tawadras was selected in an altar ballot at the end of a weeklong papal selection process that was attended by thousands of Copts.
He succeeds Pope Shenouda III, who died on 17 March.
The enthronement will take place on 18 November at St Mark.
General Bishop of the Coptic Orthodox Church in the UK, Bishop Angaelos, welcomed the selection.
Speaking from St Mark Cathedral, he said: "The atmosphere was wonderfully joyous in the cathedral, as people not only here but all over the world raised their hearts asking God's selection for our new pope and patriarch.
"There was such a euphoric reaction when the name of Bishop Tawadrous was announced, and we now shift our prayers from God's selection to God's guidance and grace upon him to lead our beloved Coptic Orthodox Church as it continues its mission to be light and salt in Egypt and throughout the world."