The 24-year-old, who Monaco paid €8.5m to sign from Flamengo in 2017, will spend the full season in Switzerland.
Basel will have an option to buy Jorge at the end of the campaign.
— FC Basel 1893 (@FCBasel1893) October 2, 2020
Jorge rarely featured after joining Monaco, but was given a run in the team after Benjamin Mendy joined Manchester City.
However, he soon fell down the pecking order and had loan spells at FC Porto and Santos back in Brazil.
With little prospect of game time at Monaco, the full-back has moved to Basel for the season.
Gremio held talks over a potential deal in June, but Jorge preferred to stay in Europe.
Jorge has won one cap for the Brazil national team, his only appearance to date coming against Colombia in 2017.
He has received two call ups since then, most recently in September 2019, but was an unused substitute.