The 24-year-old, who was a boyhood Newcastle fan, can also play at left-back and had been linked with West Ham and Aston Villa.
Colback is understood to have signed a five-year deal at St James' Park.
The former England U20 international signed professional terms with Sunderland six years ago following a spell in the club's youth academy. He scored the final goal in Sunderland's 3-0 win at Newcastle in February.
He made over 100 appearances for Sunderland and also played 50 times for Ipswich over two loan spells at Portman Road.
Paul Bracewell was the last high profile player to join Newcastle directly from Sunderland in 1992.