The 28-year-old joined City at the age of seven and signed a professional contract with the club, but he did not make a senior appearance for them.
Manchester-born Clayton will face his former side when Boro host City in their FA Cup quarter-final on Saturday.
"City shaped the way I play football. Without them, I don't know where I'd be today," he told BBC Tees.
"It's not like I feel I use to play for City now, it was so long ago, but they definitely had a hand in making me who I am," said Clayton.
"I've played in many foreign countries and gained valuable life experience with them, so I'll be forever thankful to the coaching staff that brought me through."
Saturday's match against Pep Guardiola's men may test some of his family's loyalty.
"My mum's side are big City fans, I'd like to think she would be supporting me in the Middlesbrough end," said Clayton.
He jokingly added: "She best do, otherwise I'll need to have a word with her."
Former Leeds and Huddersfield player Clayton recently signed a new Boro contract until 2021.
Asked what he wanted to achieve at the club in those four years, Clayton said: "I hope there's a good 100 appearances in the Premier League. Maybe a Wembley final might be in there as well."
Middlesbrough midfielder Adam Clayton says his time at Manchester City has shaped his career.