Colback will cross the Tyne-Wear divide, having been out of contract at the end of the Premier League season.
The versatile 24-year-old, who was born on Tyneside but came through the youth ranks at Sunderland, has agreed a long-term deal at St James' Park.
Colback helped Sunderland to a league double over Newcastle last season, scoring in a 3-0 away success in February.
After making the controversial move to Newcastle, Colback expressed his hope that Sunderland fans would understand his decision to switch allegiance to his boyhood club.
"To come to the team I supported as a boy, my hometown team, will be really special for me," Colback told Newcastle's official website.
"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.
"I've only got good things to say about Sunderland. They gave me my chance and I want to thank the fans and the club for all their support.
"I hope they can understand the chance I've had here to move to my boyhood club. Now I can't wait to pull on the black and white shirt at St James' Park for the first time."
Newcastle manager Alan Pardew is confident that Colback's skills in possession will improve his side's midfield.
"I'm extremely pleased to have brought Jack to Newcastle United," Pardew said.
"He's a great passer, versatile and rarely gives the ball away. He's also a local lad and knows exactly what playing for this club means.
"And at 24 years old, his best years are ahead of him so I think he'll be a big asset to us."
Colback becomes Newcastle's second close-season signing following the capture of Ayoze Perez from Tenerife last Friday.
Sunderland issued a statement of their own, claiming Colback's exit had left a "bitter taste".
"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," read the statement.
"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."
