"Martin and I spoke earlier this month about his decision to retire from the international game," Woodward said.
"I made it clear during the Rugby World Cup that I would have liked him to captain England in our defence of the Grand Slam but I fully support his decision."
Woodward added: "I can't speak highly enough of Martin.
"He has made an outstanding contribution for his country both as a player and as captain on and off the pitch.
"He stands down now having achieved everything there is to achieve as an England player and I hope he will be involved in some other capacity in the international team in the future. I wish him all the best."
Commenting on Johnson's contribution to the sport in England, the Rugby Football Union's President Robert Horner said: "Not only has Martin been an inspiration to his fellow England players but also to every schoolboy who dreams one day of following in his footsteps and captaining his club and country."
Francis Baron, RFU chief executive added: "It's not every day a sport has the privilege of having an international captain with such admirable leadership qualities and talent.
"Martin has led by example and will always command great respect in all corners of the sport."