Villa will link-up with former Barcelona team-mate Andres Iniesta and ex-Germany forward Lukas Podolski.
The 36-year-old scored 80 goals in 124 games for New York after becoming the club's first ever player when he signed from Atletico Madrid in 2014.
With Spain, he won the 2008 European Championship and the 2010 World Cup.
Villa, who said on Wednesday he will leave New York on 31 December when his contract expires, announced his move to Kobe on YouTube.
"The moment has come," he said. "It's decided. I have a new destination. A great challenge awaits. Asia. New trips. New country. New culture. New team-mates. Hello Japan. Hello Vissel Kobe."
Starting his career at Sporting Gijon, he joined Real Zaragoza and then Valencia, before a £34m move to Barcelona in 2010, where he won the Spanish league twice and the Champions League.
He left for Atletico Madrid in 2013, helping them win La Liga for the first time since 1996 with 13 league goals.
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