"[He] ends a brilliant 15 seasons at the Mestalla, in which he won two La Liga titles, a UEFA Cup, a European Super Cup, a King's Cup and a Spanish Super Cup," Valencia said in a statement on their website.
The club said the reasons for not extending Albelda's contract were explained to the 35-year-old at a meeting earlier on Monday attended by new president Amadeo Salvo and coach Miroslav Djukic, who played alongside Albelda.
Former Serbia coach Djukic was appointed to replace Ernesto Valverde last week.
"Valencia wish David Albelda, one of the most important players in the history of the team and a living legend of 'valencianismo', the best of luck in his future professional career and his personal life," the club added.
"Albelda leaves an indelible mark on everyone connected with Valencia and at the club, which will always be his home."
He has played almost his entire career at Valencia, and also won 51 caps for Spain, competing at the World Cup in 2002 and 2006 and at Euro 2004.
The locally-born player was a central figure in the Valencia side that reached the Champions League finals in 2000 and 2001 and Rafael Benitez's team which won La Liga in 2002 and 2004.
Valencia also beat Olympique Marseille 2-0 to win the 2004 UEFA Cup.
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