The La Liga club announced last month that an agreement in principle had been reached that would see the midfielder move back to the Ramon Sanchez Pizjuan on a three-year contract.
Sevilla agree deal with Amavi
Inter have now ratified the deal, which will reportedly see them earn €9million.
Banega moved to the San Siro as a free agent in 2016 but struggled to settle in Serie A, making just 22 starts in all competitions for the club.
The 29-year-old, who won back-to-back Europa League titles with Sevilla in 2014-15 and 2015-16, had reportedly been a target for former head coach Unai Emery at Paris Saint-Germain.