The 26-year-old's move to Camp Nou was confirmed on Monday after a month of rumours that he would be brought on board by new boss Luis Enrique.
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"It's time to thank Rakitic for his commitment, professionalism and his Sevillismo," Emery wrote on his personal website.
"He was an example both on and off the field and, for me, it has been an honour to coach a player like him.
"It is true that people are leaving but Sevilla will always be here. Ivan is well worth being part of its history. Thank you, Ivan, and good luck!
"Meanwhile, the club is working hard to find another Rakitic and we can welcome two good players like Aleix Vidal and Denis Suarez, who are young and hungry."
Rakitic arrived in Andalucia from Schalke in 2011. He led Sevilla to the Europa League title in 2013-14 and joins Barcelona for a fee of around €20 million (£16m).