"After much thought, I have made the decision that it will be best for me to take the captaincy away from John Terry," Capello said in a statement.
"As a captain with the team, John Terry has displayed extremely positive behaviour. However, I have to take into account other considerations and what is best for all of the England squad.
The alleged affair only became public after the High Court last week lifted an injunction secured by Terry's lawyers to prevent reporting of the affair.
Perroncel, 33, had just made an appearance in front of reporters with her publicist to announce she would not be selling her story to the press when she heard of Capello's decision.
She looked shocked and mouthed: "Oh my God... he's been dropped" as the news broke.
Prime Minister Gordon Brown said he thought football fans would support the Italian's judgement.
"This decision must be for the manager and Mr Capello has made that decision. I think people will abide by that decision," he said.
Terry had been strongly backed by his club coach Carlo Ancelotti, who has insisted that the player's private life will have no bearing on his position as Chelsea skipper.
But it appears that Capello had made up his mind before a meeting that reportedly lasted only 12 minutes and finished with Terry, who he picked as captain in August 2008, in a distraught state.
"Grazie, Signor Capello" -- "Thank You, Mr Capello" in Italian -- was the front page headline in the Daily Mail, while the Sun said: "Capello Has Got It Right".
Capello was greeted by a huge media scrum at Heathrow airport on Thursday, following his return to England from Switzerland, where he had been recuperating from knee surgery.
The head coach was briefed by his assistant Franco Baldini on Thursday and had been expected to have a lengthy discussion with Terry on issues including whether he and Bridge could play in the same squad and the possibility of further embarrassing revelations in the run-up to the World Cup.
Compounding the pressure on Terry, a report in Friday's Daily Mail claimed that an associate of his management agents had offered to rent his personal box at Wembley stadium for a "cash" payment of 4,000 pounds (6,200 dollars).
The 12-seat box is one of Terry's perks as England captain and FA rules expressly forbid him from renting it to a third party. His spokesman denied that the player was involved in the alleged attempt to sell seats in the box.