The 31-year-old, capped 78 times since his debut in 2003, issued a statement on Sunday night saying his position had become untenable due to an FA hearing into allegations that he racially abused Anton Ferdinand which began on Monday.
Hodgson controversially selected Terry over Anton's brother Rio Ferdinand for Euro 2012, citing "football reasons" - Rio's injury problems - for the decision rather than the race issue.
"I'd like to thank John Terry for his commitment to the England team since I became manager," said Hodgson in a statement.
"I am of course disappointed to lose a player of John's international experience and exceptional ability.
"I have enjoyed a good relationship with John during my time as England manager and I reluctantly accept his decision.
"I can also confirm that he had the courtesy to call me prior to announcing his retirement from the England team.
"I'd like to wish John well for the future with Chelsea."
The Blues captain denies the allegations against him. He was cleared by Westminster Magistrates Court in July despite admitting uttering the words "f****** black c***" during a match against QPR last October.
He claimed it was used as part of a denial after he believed Ferdinand had accused him of using those words.
"I am today announcing my retirement from international football," the former England captain said in his statement.
"I would like to thank the England managers who have selected me for my 78 caps.
"I have had great pleasure in sharing that honour with all the players that I've played with. I would like to thank them, the fans and my family for their support and encouragement during my international career.
"Representing and captaining my country is what I dreamed of as a boy and it has been a truly great honour. I have always given my all and it breaks my heart to make this decision."
The FA stated: "The FA would like to thank John Terry for all of his efforts with the national team over the past decade.
"During his 78 appearances John has always given his full commitment to the team."
His first England cap came against Serbia and Montenegro in 2003 and he was selected for the Euro 2004 finals in Portugal.
Terry's leadership qualities persuaded former England manager Steve McClaren to give him the captain's armband after David Beckham gave up the position following the 2006 World Cup.
It was a role he took on with pride, although his England captaincy was not without its problems.
The Chelsea stalwart, who regularly put his body on the line for his country, had the armband taken away by Fabio Capello in 2010 after revelations about his private life.
Terry courted controversy at the World Cup finals in South Africa when he hinted that the players were bored at the team's base and that had held clear-the-air meetings with Capello.
After regaining the position due to Rio Ferdinand's injury problems he lost it again over the Anton Ferdinand allegations, an FA decision that led Capello to quit.
England won 50 of the 78 matches in which Terry appeared, losing just 10. He scored six goals, including the first ever senior goal for England at the new Wembley Stadium in 2007.
Liverpool's Steven Gerrard is the current England captain.