Terry, 29, held talks with England boss Fabio Capello at Wembley on Friday.
“After much thought I have made the decision that it will be best for me to take the captaincy away from John Terry,” said Capello in a statement.
Terry, who has been replaced by fellow defender Rio Ferdinand, said he abided by Capello’s decision to demote him.
“I fully respect Fabio Capello’s decision,” the Chelsea centre-half said in a statement. “I will continue to give everything for England.”
Capello returned to the United Kingdom on Thursday and is thought to have been keen to resolve the Terry saga before travelling to Poland for Sunday’s Euro 2012 draw.
The 59-year-old Italian, who has been recovering from knee surgery in Switzerland, has been monitoring the fall-out closely and regularly spoken to his trusted lieutenant Franco Baldini.
Baldini, England’s general manager, held in-depth talks with four key Football Association board members on Monday – chairman Lord Triesman, chief executive Ian Watmore, director of communications Adrian Bevington and head of development Trevor Brooking.
They agreed that Capello alone would make the decision about Terry’s future and that the priority was to make the right decision rather than a quick one.
“As a captain with the team, John Terry has displayed extremely positive behaviour,” read Capello’s statement.
“However, I have to take into account other considerations and what is best for all of the England squad.
“What is best for all of the England team has inspired my choice.
“John Terry was notified first.
“When I chose John Terry as captain, I also selected a vice-captain (Ferdinand) and also named a third choice. There is no reason to change this decision.
“I would like to take this opportunity to thank the FA, particularly Lord David Triesman and Ian Watmore for allowing me to make this decision in my own time and in the best interest of the team.”
England’s next match is a home friendly against Egypt on 3 March as they continue their preparations for the World Cup in South Africa.
They will be lead out in that match by Ferdinand, with Liverpool midfielder Steven Gerrard moving to vice-captain.
Ferdinand, 31, is currently serving a four-match ban for violent conduct after only just returning to action following a three-month lay-off because of a back injury.
The Manchester United defender will hope to continue the form shown by England following Terry’s appointment in August 2008.
In the 15 matches in which he wore the armband under Capello, England won 11 and drew two, qualifying easily for this year’s World Cup.
A married father of twins, Terry is alleged to have had an affair with Vanessa Perroncel, the former girlfriend of England and former Chelsea team-mate Wayne Bridge.
Bridge, who has a son with the French model, moved to Manchester City in January 2009 and is recovering from a knee injury that has kept him out of action for the last two months.
Meanwhile, Perroncel, a lingerie model and former nightclub hostess, said she would not be selling her story.
In a statement read on her behalf by publicist Max Clifford, Perroncel said: “I have decided I do not want to speak publicly about the speculation since it only seems to add more fuel to the fire.
“I have a three-year-old son and he is my main concern. I do not believe speaking to newspapers or the media is in his interest or my own.”