Cole's season was curtailed by a knee injury against Charlton in February but 10 goals in 21 starts were enough to convince Stuart Pearce the 34-year-old was worth another contract.
"It was good to get the goals 'early doors' last season," Cole told City's official website. "People were a bit sceptical but I like to think that I won them around, and the fans have been very supportive of me since I came here.
"I set myself a target and I was well on course to get to that when I was injured, so that left me very disappointed, but I honestly believe that I would have got to my target. Hopefully this season I will get to the target I have set for myself, and a lot quicker."
Cole is still recovering from his injury but is confident he'll be ready for the start of next season.
"I'm getting there," he added. "I want to get through pre-season unscathed but my main aim is to be ready for the first game of the season, home or away, whoever it's against."
Meanwhile, Pearce has made contact with Ajax full-back Trabelsi regarding a move to City.
The 29-year-old Tunisia international is available on a free transfer but offset that by asking for wages above City's limit of £30k per week.
He will aim to prove he is worth that much at this summer's World Cup with Tunisia and also impress the likes of Spurs, Inter Milan and Paris St Germain, who are already interested.
Pearce is on his way to Germany too to work for ITV as an analyst and also to scout the lesser-known countries for potential signings.