Villa, 36, departs MLS after scoring 80 goals in 124 appearances for NYCFC. He paid tribute to everyone associated with the franchise, as well as to the team's fans in avideo on YouTubelast week as he said his goodbyes.
Vissel Kobe chairman Hiroshi Mikitani said: "We are pursuing a new style of play and after talking with the coach, Villa's name came up as a striker who would fit that style of play. He is a wonderful striker."
The forward spent four seasons with the club as its first captain but has now opted for a new challenge in Japan, where Iniesta has been playing since May.
"It's decided," he said in a video before Kobeannounced the move. "I have a new destination. A great challenge awaits.
"New country. New culture. New team-mates. Hello Japan. Hello Vissel Kobe."
A statement from the club read: "By adding Villa to its roster, Vissel Kobe aims to build on the foundation laid with the additions of Lukas Podolski and Andres Iniesta, as it takes another step towards the club's goal of becoming the number one club in Asia."
Villa, Spain's all-time top scorer with 59 goals, won the European Championship and World Cup together with Iniesta, while they also picked up two La Liga titles as well as the Champions League, the Copa del Rey, the UEFA Super Cup and the FIFA Club World Cup at Barcelona.
Kobe, who signed Iniesta in May, are owned by Rakuten, a Japanese e-commerce giant that is also Barcelona's shirt sponsor. The club have endured a difficult season butIniesta scored on Saturday as Kobe wrapped up their J.League campaign with a 3-2 victory over Vegalta Sendai, finishing 10th in the 18-team league.
Villa becomes the third World Cup winner at Kobe with former Germany international Lukas Podolski also at the club.
Information from John Duerden was used in this report.
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David Villa bids farewell to NYCFC - Via MLS
David Villa announces he is ready for another challenge as he bids farewell to New York City FC.