"I am going to leave on June 30. I want to develop as a player and try something new," the 27-year-old told a news conference, ending any hopes the La Liga club may have had of changing his mind.
The powerful centre forward, nicknamed the Lion King, turned down the offer of a new contract during the closed season and said he wanted to leave, but Bilbao refused to negotiate with interested parties.
Coach Marcelo Bielsa relegated last season's top scorer to the bench when they reached the final of the Europa League and Copa de Rey and Llorente has started only once in La Liga this term and has one goal to his name.
"It isn't about money because the offer the club made was irresistible," Llorente added.
"The media have not helped with the negotiations and it is one of the things that has generated the bad atmosphere around me out on the pitch. This has encouraged me not to renew my contract; this and many other things.
"I took the decision when I went out for the first Europa League game at San Mames (in August).
"Most of what has come out in the press is lies and this has turned people against me. This has meant when I run out on to the pitch people whistle at me. There is a sector of the crowd who do not want me but I feel loved by the majority."
Llorente, who was linked with interest from Juventus over the summer, came through Bilbao's youth academy before making his first-team debut in January 2005.
A member of the Spain squad that won the World Cup in 2010 and Euro 2012, he netted 17 goals in 32 league appearances for Bilbao last season, and scored seven in 15 games in European competition