The 24-year-old has signed a long-term contract at St James' Park, with his contract at Sunderland due to expire this summer.
Colback, a former England under-20 international, made over 100 appearances for Sunderland and played in their League Cup final defeat to Manchester City in March.
"I'm absolutely delighted," he told Newcastle's website. "To come to the team I supported as a boy, my hometown team, will be really special for me.
"It was an opportunity I couldn't let slip. If you asked fans around the world the one thing they'd like to do before they die, it would be to play for the team they support and I've got the chance to do that."
However, a statement released on Sunderland's website registered their disappointment in Colback's decision and conduct.
“Jack is a player we have nurtured and developed through our academy system since he was eight years old. We gave him the opportunity to become a professional footballer and are therefore extremely disappointed in the events that have led to his departure from the club.
“This wasn’t about money - the club agreed to all of the terms demanded of us during discussions and we were always led to believe that Jack wanted to stay with us. At his and his representatives’ request, final talks were put on hold until the club secured its top flight status. To our dismay however, we were subsequently never given the chance to negotiate with him to stay.
“For him to then leave the club that has supported him throughout his formative years in such a manner, with no chance for Sunderland to recover any of the significant investment that it has made in him as a player, has left a bitter taste."
- Sports & Recreation