The Spaniard will move to the Stadium of Light on July 1 upon the expiry of his contract at Championship side Wigan Athletic.
Gomez, a youth product at Barcelona, moved to Catalan rivals Espanyol in 2007 and spent two years at Estadi Cornella-El Prat.
Roberto Martinez brought Gomez to Britain when he signed him on a season-long loan for Swansea City in June 2008.
After impressing at the Liberty Stadium, Martinez once more recruited Gomez for Wigan ahead of the 2009-10 season.
During his time at the DW Stadium, Gomez collected the FA Cup in 2013 and notched on 11 occasions during his final season on Lancashire.
Sunderland head coach Gus Poyet has started his close-season recruitment early, with 29-year-old Gomez marking the club's second recruitment following full-back Billy Jones' arrival from West Brom.
It comes as further good news for the Wearsiders after Poyet himself signed a new deal until 2016 on Wednesday.
