Barca said in a statement they would receive 35 million euros (31.5 million pounds) for the 30-year-old Cillessen, earning a considerable profit on the Dutchman who they signed from Ajax Amsterdam for an initial fee of 13 million euros in 2016.
Cillessen played 32 times in three seasons for Barca, never managing to unseat German Marc-Andre ter Stegen as the club's number one goalkeeper.
He was regularly picked as first choice in the Copa del Rey, however, lifting the trophy twice with Barca but he was on the losing side in last season's final which Valencia won 2-1 to end an 11-year wait for a trophy.
Valencia said Cillessen's contract would contain a buy-out clause of 80 million euros.
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Cillessen has been capped 50 times by the Netherlands and is their first-choice keeper.
(Reporting by Richard Martin, editing by Ed Osmond)
