The Swans announced the acquisition of the Spaniard on their official website.
Llorente arrives after a difficult season at the Ramon Sanchez Pizjuan Stadium, with Kevin Gameiro ahead of him in the pecking order.
The 31-year-old started just 20 games in all competitions, scoring seven goals and assisting five.
Bleacher Report UK's Sam Tighe is nevertheless anticipating his arrival at the Liberty Stadium:
The Spaniard has been fairly prolific throughout his career, netting 27 goals in two seasons at Juventus and scoring more than 100 for Athletic Bilbao.
Llorente possesses the physicality that should allow him to adapt well to the Premier League, and his aerial prowess will give the Swans an added dimension in attack.
His hold-up play is a particular strength, and he'll look to bring the likes of Jefferson Montero into the game.
Swansea have struggled for goals since selling Wilfried Bony to Manchester City—they scored just 42 in the Premier League last year, better than only six other teams.
With the addition of Llorente, the Swans should be more potent in the final third.