Terry, who is attending a disciplinary hearing over a charge he used racist language towards QPR defender Anton Ferdinand, had phoned Hodgson to inform him of his decision.
It is understood that Hodgson tried to persuade him otherwise but Terry - who denies the charge - was adamant it was "untenable" for him to play for England with the FA pursuing the case. Hodgson released a statement on Monday saying he "reluctantly accepts" Terry's choice.
He said: "I'd like to thank John Terry for his commitment to the England team since I became manager. 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 announcement his retirement from the England team. I'd like to wish John well for the future with Chelsea."