The 24-year-old was free to sign a long-term deal at St James's Park with his contract at Sunderland due to expire this summer but the Wearsiders were angry at the circumstances of his departure.
Sunderland said they had met his demands, and were led to believe he wanted to stay, only for the former England under-20 international to change his mind.
"Jack is a player we have nurtured and developed through our academy system since he was eight years old," the club said in a statement on their website (www.safc.com).
"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."
Sunderland said they had put contract talks on hold, at Colback's request, until the club's top flight status was assured and were dismayed not to have been given a further chance to negotiate.
"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," they said.
Colback, who made more than 100 appearances for Sunderland and played in their League Cup final defeat to Manchester City in March, said the prospect of playing for Newcastle was too great to turn down.
"I'm absolutely delighted," he told their website (www.nufc.co.uk). "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."
(Reporting By Sam Holden, editing by Alan Baldwin)
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