The Welsh international arrived at the Stadium of Light in a £2 million deal after spending four years with the Hoops.
The 23-year-old has signed a four-year deal with the Black Cats and is determined to test himself at Premier League level.
He told Sky Sports: "I have been at Celtic for four years and enjoyed every minute of it but I spoke to my agent and it seemed to be a good move for me at this stage.
"I'm happy to move forward and playing in the English Premier League was a big factor in my decision - Sunderland are a massive club, there is no doubt about it.
"It was a hard decision, I had grown close to a lot of the boys at Celtic but I just felt I needed something new. I think I have made the right decision. Celtic are a great club and I wish them all the best for the future."