The 28-year-old will call an end to a five-year stay at the DW Stadium after reportedly turning down a contract offer from the Latics and will now officially join the Premier League side on July 1.
The midfielder came from the youth ranks at Barcelona before joining Espanyol in 2007.
A loan spell at Swansea City under Roberto Martinez saw the Spaniard follow his counterpart to Wigan in the summer of 2009, with whom he won the FA Cup with in 2013.
Gomez becomes Sunderland's second signing of the summer following Billy Davies's free transfer from West Brom.
It comes as further good news for the Wearsiders after Poyet himself signed a new deal until 2016 on Wednesday.