The 24-year-old joined the European champions for £35m on Monday, having spent eight years with the Gunners.
"The easiest thing would have been to stay at Arsenal," he told Barca TV.
"I thought I'd stagnated a bit, and needed a change of scenery. I needed a special motivation to bring the best out of myself."
The Spanish international has already won his first major honour with the Catalan side after Wednesday's Super Cup win over rivals Real Madrid.