Terry, who is due before a Football Association tribunal on Monday facing a charge of racially abusing Queens Park Rangers defender Anton Ferdinand , announced on Sunday he was quitting international soccer.
The former England captain, capped 78 times in an international career stretching back to 2003, said the impending case against him had made his position in the national team untenable as he was cleared in the criminal trial over the affair.
"I'd like to thank John Terry for his commitment to the England team since I became manager," Hodgson said in an FA 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."
If found guilty by the FA of abusing Ferdinand, Terry could face a lengthy ban similar to the eight-game suspension served by Liverpool's Luis Suarez last season for racially abusing Manchester United's Patrice Evra.