Llorente, who won the 2010 World Cup and 2012 European Championship with his country, joins the Swans on a two-year deal from Sevilla.
The transfer fee was not disclosed.
"The striker, who will wear squad number nine, has signed a two-year contract at the Liberty Stadium after undergoing a successful medical," read an official Swansea statement.
Llorente spent just one season with Sevilla, following a lengthy stint with Athletic Bilbao and two years at Juventus, where he won two Serie A titles.
The 31-year-old has scored over 130 goals in his career.