The 29-year-old former Valencia man, who has four Spain caps to his name, has long been expected to make the switch after not featuring for Swansea during pre-season.
And the Welsh club confirmed his move on Thursday, along with the departure of Chico Flores to Lekhwiya after the defender had already made his future clear in an open letter.
Hernandez arrived in south Wales from Getafe in 2012 and has since scored five goals in 57 Premier League appearances.
Highlights of his Swansea career include winning the League Cup in 2013 and reaching the last 32 of the UEFA Europa League.
Hernandez follows in the footsteps of Chico and former Swansea manager Michael Laudrup, who was dismissed by the Premier League side in February, in making the move to Qatar.
Swansea expressed their gratitude to the departing duo in a short statement on their website.
"Everyone at Swansea City would like to thank Chico and Pablo for their service, and wish them well in their new challenges," the statement said.
