The former England goalkeeper was signed by Ange Postecoglou in 2021 from Tottenham Hotspur, marking a turning point in his career.
At Celtic, Hart became a fan favourite, winning seven major honours, including three Scottish Premiership titles.
Speaking to BBC Sport, he said: "There's no shoulda-woulda-couldas with Celtic. That place just felt right. Everything about it.
"To get the opportunity to go first and foremost, when football was about to turn its back on me, was one of the best last lifelines that I ever was given."
Reflecting on the crossroads in his career, Hart noted how he was determined to prove himself at Celtic, despite being on the bench at Spurs.
He said, "I thought I had life left in me. I really did think I had life left in me, and I knew that it was a difficult place to go to prove myself, you know, because Celtic demands excellence.
"So, I had a lot to prove, and I knew that. And I knew this football club wasn't daft. And the way the relationship grew, I honestly couldn't have asked for more."
As he approached his retirement, the 37-year-old remained steadfast in his decision not to play for another club.
He said, "I had life left in me. I was 37. There's no doubt I was physically capable of carrying on, but I didn't want to play for anyone else after that amazing opportunity that I was given.
"To have that last home game and the Green Brigade's farewell that was given to me after half-time when I walked out, I swear, I never... I still feel it now.
"So, I think I've said it enough about what it means to me, so, forever grateful."