L'Equipe suggest that Drogba is relishing the opportunity to work with Jose Mourinho once more following his free transfer from Galatasaray.
Chelsea have lost striking options in Demba Ba and Samuel Eto'o so far this summer, and 36-year-old Drogba is always likely to offer goals.
The news broke ten years to the day that Drogba originally signed for the club from Marseille.
Ivorian striker Drogba - who in 2012 left West London for an ill-fated spell in China before moving to Turkey to play for Galatasaray for a season and half - is regarded by many Chelsea fans as one of the greatest players in the club’s history.
Dorgba was the hero when the club won the 2012 Champions League final against Bayern Munich - scoring a late goal that sent the match into the extra-time and then winning penalty in the subsequent shoot-out.
Drogba also won three Premier League titles, four FA Cups and two League Cups at Chelsea, scoring 157 goals in 341 appearances in eight years.