The Danish striker, who endured loan spells at Sunderland and Juventus over the past two seasons, failed to find a new club during the summer and has been focussed on making a return with the Gunners.
Bendtner was part of the team that beat West Bromwich Albion in the Capital One Cup on Wednesday, and he has praised the Arsenal fans for their support.
"Very emotional return, but what better way than with a win!" Bendtner posted on Instagram. "Fans [were] absolutely incredible throughout the game and help us in difficult periods.
"For myself I was very moved by my reception and hearing my song again made my heart skip! Young players did ever so well and kept [their] cool in a difficult penalty shootout. Respect! Skipper looking fresh!"
Bendtner was the first Arsenal player to score a spot kick as they prevailed 4-3 in the shootout at The Hawthorns.