The 21-year-old has verbally agreed on personal terms over a six-and-a-half-year deal and is in the process of scheduling a medical ahead of a move to west London.
The remaining details are being finalised but the central defender is now expected to complete his move to Stamford Bridge with the January transfer window now open.
The France international had just 18 months left on his deal at the Ligue 1 club allowing Chelsea to agree on a deal with a favourable fee in just a few days.
Graham Potter will add the left-sided defender to his options with Wesley Fofana and Ben Chilwell still injured.
Thiago Silva, 38, is also yet to sign an extension on a contract that expires in the summer.
Badiashile is expected to be the third signing of the January transfer window for Chelsea following the announcement of a £8.6m deal for 19-year-old striker David Datro Fofana. Teenage midfielder Andrey Santos is also in London completing a £20m move from Vasco.
Chelsea remain interested in doing further business and are in talks to complete a record £105m move for Benfica midfielder Enzo Fernandez.
Talks have slowed amid negotiations to spread payments over multiple seasons to avoid FFP (Financial Fair Play) sanctions.