It had been suggested throughout the 2013-14 campaign that Wenger would leave the club, bringing to an end an 18-year stint in charge following his arrival in 1996.
Some sections of Arsenal fans were beginning to become restless with their lack of silverware, with Arsenal going nine years without a trophy until Saturday's FA Cup final victory over Hull City ended that drought.
"He was always staying," Harris told the London Evening Standard.
"There was never any doubt. He gave us his word back in the autumn, just after the season started.
"It was just a case of sorting it out. It was the press making all the problems."
"If he wins the league and the cup and the Champions League in the next three years, then I'm sure he will stay," he said.
"Three years is a long time in football so let's see what happens. It's very hard to follow someone like (Alex) Ferguson (who left Manchester United in May 2013 following 26-and-a-half years at Old Trafford) and I'm sure it will be very hard to follow Arsene."
