Isaac, who also plays as a striker and has spent time at Chelsea's academy, will join up with the club's U19s as he bids to break into the senior squad.
His father, Didier, enjoyed an immensely successful time at the Ligue 1 club before moving to Marseille then Chelsea. Drogba scored 164 goals in 381 appearances for the Blues.
"Couldn't be more proud of you Isaac Drogba," the 39-year-old wrote on Instagram.
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