Arsene Wenger's side cemented its fourth-place finish with a composed victory against the Magpies, with the match-winning goal coming from the French center back.
The Gunners' victory meant that regardless of how Tottenham got on against Sunderland at White Hart Lane, they would be the North Londoners appearing in the Champions League come September.
Newcastle marked Steve Harper's final game by handing him the captaincy for the day, as the goalkeper reached the end of a 20-year spell at the club. The 38-year-old was afforded a marvelous sendoff by Newcastle's supporters as they chanted his name for the duration of the 37th minute, to symobolize the goalkeeper's shirt number.
Newcastle barely touched the ball in the opening five minutes as Santi Cazorla and Aaron Ramsey dominated possession in midfield for the visitors, and that impressive spell was only broken by a thunderous challenge from Cheick Tiote on Tomas Rosicky.
The hosts fashioned the first chance of the game in the 10th minute when Papiss Cisse fired just over after strong play down the left-hand side from Mapou Yanga-Mbiwa.
Alan Pardew's side continued to threaten down the flanks, as Hatem Ben Arfa and Yoan Gouffran enjoyed themselves playing in an attacking three off Cisse.
Wenger's decision to start Mikel Arteta despite a calf injury he picked up against Wigan during the week backfired shortly before the half-hour mark, as the former Everton midfielder had to be replaced by Alex Oxlade-Chamberlain.
Arsenal appeared to click through a couple of gears at the start of the second half, as Theo Walcott and Cazorla began to run at Newcastle's defense, and in the 52nd minute the Gunners' pressure paid off when Koscielny gave them the lead. The Frenchman was on hand to smash a close-range volley past Harper after Theo Walcott's free kick sat up for him inside the Newcastle penalty area.
Just moments after going ahead the Gunners were fortunate not to concede a free kick in a very dangerous position, as the ball struck Ramsey's arm as he slid to dispossess Ben Arfa in full flight. Despite being just yards away from the action, referee Howard Webb waved play on.
Newcastle withdrew Yohan Cabaye shortly after, and that sapped the life from the hosts' play as Arsenal bookended its performance by dominating possession in a similar vein to how it started the game, finishing off the quest to return to the Champions League.