The 19-year-old striker, who has represented both the United States of America and England at youth level, would have seen his previous contract expire at the end of this season, putting a number of clubs both home and abroad on the alert.
Balogun has made a breakthrough into the Arsenal first team this season, scoring twice in six appearances across all competitions.
He is yet to make his Premier League debut, with the Pierre-Emerick Aubameyang, Alexandre Lacazette and Eddie Nketiah ahead of him in the pecking order.
"My ambitions for next season are to make an impact in the first team. I see it as something that I've taken upon myself to be able to go over there and make an impact, not just be one of the numbers,” Balogun said after signing his new deal.
"I want to be somebody who eventually leads that group, so I would say I have quite driven ambitions. We'll see if I can make them happen."
Gunners boss Mikel Arteta added: "We have been extremely impressed with Flo this season.
"He has continually shown his natural ability in many training sessions with us and we have been equally impressed with his early integration into the first-team squad on matchdays.
"He has given us glimpses with the performances and of course with his two goals already for the first team. The hard work starts here for Flo and we are all looking forward to supporting and working with him in the years to come."
