The 25-year-old Denmark forward has found himself slipping out of the first-team picture over recent campaigns, resulting in him being loaned out to Sunderland and then Juventus, where he suffered a thigh injury and failed to score a goal.
Bendtner had been lined up to join first Eintracht Frankfurt earlier this summer, but could not agree personal terms with the German club - with his current Arsenal deal worth a reported £52,000-a-week.
Both newly promoted Hull City - managed by Steve Bruce, who had the striker on loan at Birmingham City as a raw talent in 2006/07 - and Crystal Palace were also keen to try to broker a deal.
Arsenal looked to bring in some attacking cover on deadline day, when they broke the club record transfer with a £42.2m deal for Mesut Ozil, but they could not push though a loan deal for Demba Ba with Chelsea, which led manager Arsene Wenger to decide against letting Bendtner leave.
While clearly disappointed he could not get a "fresh start" somewhere else, Bendtner, who is currently regaining full match fitness, maintains if called upon he would be ready to throw himself back into action in an Arsenal shirt for the first time 20 August, 2011.
In a statement released by the player's representatives, International Football Management, Bendtner said: "It is no secret that Arsenal and myself had agreed that I could leave the club during the 2013 summer transfer window, subject to an agreement between all parties.
"An agreement had been reached with more than one club this week, but as Arsenal were unable to secure the services of another striker, they reserved their right to not sanction any deal to be concluded.
"Naturally, I was very disappointed as I was looking forward to a new challenge, with a new club and a fresh start in English football.
"Many things have been said about my where my future lies after many years at Arsenal; the truth is I just want to play football which is when I am happiest and Arsenal is a fantastic environment for any professional to apply their trade.
"I still feel very strongly about Arsenal Football Club and following positive talks with the manager, I am looking forward to working hard to regain full fitness and doing my very best to help the team and the manager fulfil our objectives and ambitions this season.
"I have learnt a lot from my loan experiences at Sunderland and Juventus, and I want to assure all Arsenal fans that I will give everything I have to contribute to what I believe will be a successful season for the club."