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In a statement on their official website the Catalans confirmed they had signed the 27-year-old on a five-year contract for a fee of 13 million euros (£11.1 million, $14.7 million), rising to a potential 15 million euros.
Barca said Cillessen flew to Spain on Thursday morning to undergo a medical and would be officially unveiled on Friday.
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Cillessen made a farewell appearance for Ajax on Wednesday in their 4-1 Champions League play-off defeat to Rostov in Russia.
His arrival cleared the way for Chilean goalkeeper Claudio Bravo to leave the Camp Nou for Manchester City, leaving the Dutchman to compete with Marc-Andre ter Stegen for the number one jersey in Luis Enrique’s side.
FC Barcelona announced later Thursday that Bravo had “been transferred” to City for a fee of 18 million euros, rising to a potential 20 million euros.
