The 20-year-old youth product, who joined the club at the age of nine, made 33 first-team appearances during a breakthrough campaign last season.
The length of the new contract has not been made public but is reported in the English media as a five-year deal.
Recent reports had suggested Aston Villa were bidding to sign the England Under-21 international, who has had loan spells at Huddersfield and Leipzig since making his senior debut in 2018.
"As we all saw last season, Emile is an intelligent player with excellent ability," said Gunners manager Mikel Arteta who has handed Smith Rowe the number 10 shirt.
"His sharpness on the turn and exceptional vision have already made him a key player for us. His attitude and willingness to learn have also been very impressive."