Following discussions with FA officials on Tuesday, Tuchel has officially accepted the position.
BBC Sport says everything has been settled and the German becomes the first foreign manager of England since Fabio Capello.
The move has been quick and the FA are expected to unveil Tuchel as new manager on Wednesday.
England caretaker coach Lee Carsley will remain in charge for their Nations League ties in November - Tuchel will then takeover.
Tuchel left Bayern Munich at the end of last season after failing to guide them to the Bundesliga title.