The 20-year-old attacker, named the league's best young player of 2018, was set to undergo a medical with the Spanish side and would join up with their 'B' side.
Financial details were not released but earlier reports said Barca would pay around €2 million euros for Abe, who made his senior international debut at the Copa America and appeared in all three of their matches.
"It was a difficult decision to leave (Kashima) mid-season, but I chose to make the move because I absolutely want to take on this new challenge at Barcelona," Kyodo news agency quoted Abe as saying in a statement.
Reports in the Catalan press suggest that Abe will spend the season with Barcelona's B team in the Spanish third tier.
This follows the signing of 16-year-old English striker Louie Barry from West Bromwich Albio.