In a statement, Hodgson said of his captain: "While I'm disappointed in the decision, I can entirely understand Steven's situation and can have no complaints given the incredible service he has given to his country. I must respect his wishes due to the discussions we have had and the amount of thought and consideration he himself has given it.
"He is an incredible man and a fantastic footballer who we have all been blessed to see in an England shirt so often. It is never by coincidence that people reach such a staggering figure as 114 caps, it is a mark of his wonderful talent allied to a huge drive and determination to live up to the highest standard.
"He is not only a player to bring crowds to their feet with moments of brilliance - he was a tremendous captain and an exceptional role model for everyone who was fortunate to come into contact with him. We shall miss his leadership qualities as we look ahead to the qualification campaign with a youthful group of players. I wish him all the best in the future, although I know I can count on his continued support and influence as a helpful presence moving forward."
Wayne Rooney is the early favourite to succeed Gerrard as England captain.