Nketiah looked set to leave the Emirates Stadium this summer as his previous contract would have expired at the end of this month but he took his chance towards the end of the 2021/2022 campaign, scoring five goals in Arsenal's last seven league matches.
The former England u-21 international joined Arsenal as a 14-year-old and has come through the youth ranks.
Being handed the number 14 jersey underlines how highly Arsenal regard Nketiah.
The club's all-time top scorer Henry scored most of his 228 goals across two spells in that number while in recent times, Theo Walcott and Pierre-Emerick Aubameyang have impressed while wearing it.
"I'm delighted Eddie is staying with us," a statement from Arsenal manager Mikel Arteta read on the club's website.
"He represents what we are all about and all the values of the club.
"We are very happy that he has extended his contract and now we have to get to work and continue to develop the great talent and person that we have in him."
Arsenal technical director Edu, added: "The foundations of this squad are built on young talent and in particular those who have come through our Academy system.
"Eddie was released by another club as a young man but has always shown he has the attitude as well as the ability to become a top player.
"The fact he's signed a new contract is an important part of our squad planning for next season and we're all delighted."
