Nelson's contract expired at the start of July but he was still locked in negotiations over a new deal.
Despite interest from the likes of Newcastle United and AC Milan, the Arsenal academy sees it prudent to remain at the Emirates Stadium.
Nelson came through the Arsenal youth ranks and has spent time on loan at Hoffenheim and Feyenoord in the past.
Last season he made 18 appearances across all competitions, with all his 11 games in the Premier League coming as a substitute.
Nelson scored three goals last season; his most telling effort coming as a 97th minute winner against Bournemouth in the Premier League.
Sporting Director Edu said: “Reiss is still only 23 years old but has already made a significant contribution to Arsenal for many years. He has gained good experience on loan, has come back and showed just how valuable he is to us.
"We are so happy to agree a new deal with Reiss, and we are proud that he is another young player who has developed through our Academy into our first team.”
Arsenal manager Mikel Arteta added: “Reiss is a player I have admired since the first day I was here. He has tremendous ability and is such an exciting offensive talent. Reiss knows how important he is to our squad with the quality he has.
"It’s great that Reiss has committed his future to us - he knows this club so well, he grew up here and we look forward to enjoying many more good moments with him.”
