Miller, 30, said to viewers: "From the bottom of my heart and my family's heart. This is the best thing that's ever happened to my father's son."
The actor - best known for playing Aaron Dingle in the ITV soap since 2008 - left behind his six-week-old baby son Albert and fiancee Steph Jones to take part in the reality show at Gwrych Castle in north Wales.
He told Ant McPartlin and Declan Donnelly: "I've made no secret that I wanted to do this to set him up financially for the future and I wasn't in a place to do that. Hopefully I'll be able to do that now and I've also made my family proud."
The soap star initially struggled to overcome his fear in some of the gruelling trials in the show, and kept being voted by the public to take part in more.
Joking about how he had come across on screen Miller said: "The original idea was to show them that I don't just cry on television but I think I've failed.
"I've played him [Aaron Dingle] for a long time and I wanted show a different side of myself and to have a go at the reality world and I've loved every minute of it."
And speaking about his bromance with fellow campmate David Ginola, Miller admitted he had been so excited to meet the former footballer.
He said: "He exceeded all the expectations. To spend that much time with him and then genuinely like him. I instantly bonded with him."
Meanwhile, runner-up Gregson joked that he may need to see a doctor after watching back highlights of how much he had broken wind during his time in the castle.
Asked by Ant and Dec if that was normal behaviour for him, the 47-year-old actor said: "I'm not as bad as that. I'm seriously thinking I need to see someone when I get out - it isn't normal!"
Gregson - who has played Steve McDonald in Corrie since 1989 - also revealed he had not been too scared of the Bushtucker Trials by cunningly keeping his phobia of spiders from the show producers.
He confessed: "It wasn't as bad as I thought it would because I really dont like spiders, so every time I was asked what I was I afraid of I said I 'aint telling you. So..."
Loose Women presenter and former Saturdays singer Frankie Bridge came third in the reality show, despite being the bookmakers favourite to win.
Watch: Who is I'm A Celebrity 2021 winner Danny Miller?