Gunners boss Arsene Wenger confirmed his interest in the Germany international earlier in the season but the player has committed his future to the Bundesliga champions
BVB announced that the 19-year-old had agreed to a two-year contract extension that will see him stay at his hometown club until 2016.
"Everyone knows how comfortable I feel in Dortmund," Gotze told the club's official website. "The club are far from finished with their recent resurgence, and I want to be part of this development."
Sporting director Michael Zorc was thrilled to announce the young forward's extension, the hot prospect having also attracted the interest of Manchester United and Real Madrid.
"We are very happy that we will take the next step with Mario in the future," he added.
Gotze first joined Dortmund at the age of nine. He earned his first appearance with the club's senior side at the age of 17 and within a year won his first senior international cap for Germany.
Arsenal boss Arsene Wenger had the chance to witness Gotze’s talent first-hand when the two sides met in the group stages of the Champions League earlier in the season.
Although the youngster had a limited impact in the two fixtures, Wenger was in no doubt as to the potential of the player.
|"Mario Gotze is a player for the future. It's no surprise to me that all big European clubs show interest in him, as we do also"
- Arsene Wenger
"For me, Mario Gotze is a player for the future," he told German television station SAT1 TV.
"He is very talented, has a great attitude. It's no surprise to me that all big European clubs show interest in him, as we do also."
Arsenal can be backed at 2.60 with 188Bet to be leading at half-time and full-time when they face QPR in their next Premier League match.
With Wenger’s hopes of tempting the player to the Emirates Stadium seemingly at an end, the Frenchman may well turn his attention to Lille midfielder Eden Hazard, who has been linked with a host of Premier League clubs in recent months.