Henderson finalised his switch to the Dutch side last Thursday when Saudi Arabian club Al Ettifaq agreed to end his three-year contract after just six months.
Reports suggested the former Liverpool captain would have faced a large tax bill on his earnings in Saudi Arabia if he had signed for a Premier League club but he insisted the move to Ajax was purely a sporting decision.
“Don’t believe what you read in the press,” Henderson said. “It had nothing to do with anything but football.
“I felt it was the perfect opportunity to come to such a huge club and showcase what I’ve tried to do my whole life – to dedicate myself to football.
“The welcome here has been incredible and I’m overwhelmed to be given the opportunity at a great football club and to repay the faith shown in me.
“Over the next two-and-a-half years, I will give everything to get the club back on track and to be as successful as possible.”
Reports have also claimed a desire to play more competitive football and retain his place in the England squad for this summer’s Euros played a part in Henderson’s desire to leave Saudi Arabia.
Henderson revealed: “I’m in contact with Gareth [Southgate] regularly, as I have been many years, and that hasn’t changed.
“Like he is with all the players, you know how close he is to the lads. He understands the situation.”