The Chelsea centre-back retired from international football in September, the day before an FA hearing that found him guilty of racially abusing QPR's Anton Ferdinand.
The 31-year-old claimed that his position had been made "untenable" before being banned for four matches and receiving a £220,000 fine, despite being cleared in a criminal court.
Roy Hodgson's squad are back in training ahead of the World Cup 2014 qualifier against San Marino at Wembley, before travelling to face Poland.
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Hart told reporters: "As an inspiration, a very passionate and proud Englishman. That would be the best way to sum up John as a player.
"He was someone who, when I first came into the England squad, treated me just the same as he does now. A great professional, a real inspiration football-wise and a good person as well."
The defender's retirement, along with a suspension to Glen Johnson and doubt over whether Ashley Cole will be selected following a dispute with the FA relating to Terry's charge, means Hodgson will have to swap things around at the back.
However, Hart believes the side's options are always getting better, and insisted that competition for places is a good thing, suggesting Cole will be pleased to see Everton left-back Leighton Baines come in and do well.
"Such is the nature of English football that everyone is always improving and trying to get better and that seems to be the case, which is a great thing," he added.
"If you spoke to Ashley, I think that he'd say he loves the fact that Bainesy is getting a little bit of air time and a lot of love because it is going to make him play better and harder.
"There's an opportunity to get in at centre-half. John Terry has held down a position for a long time now and maybe some people wouldn’t have seen the light.
"Unfortunately he has retired now but that gives someone else an opportunity to play."