With Barca set to sell Claudio Bravo to Manchester City, Cillessen will be competing with Marc-Andre ter Stegen for a place between the sticks.
Cillessen joined Ajax from NEC in 2011 and went on to make 100 Eredivisie appearances and won the league three times in succession from 2012 to 2014.
He arrives is Spain on a five-year contract for a fee of €13.
The 27-year-old gloveman has also been capped 30 times and garnered plenty of praise for his performances in the 2014 World Cup when he helped his side to the semi-finals.