Bacuna was expected to be on his way to the Spanish giants in a deal when he became a free agent last August.
The 21-year-old was signed by Napoli from Valencia in 2015
Reports suggested that Inter made a bid for the left-back last summer but he chose the Serie A club where he had spent his last season with Palermo.
He was released from his contract earlier this month and spent this campaign on loan at Bologna.
He scored 26 goals in 56 Serie A games for the Giallorossi, but the club have now confirmed that he has completed a formal move.