"I'm moving from Ukraine to France. Hello @s_c_bastia !" Inkoom wrote on his Twitter feed on Friday.
Inkoom's move will be official once the Corsican club have received administrative documents from their Ukrainian counterpart, president Pierre-Marie Geronimi told a news conference. Ukraine's transfer window lasts another month.
Full-back Inkoom was omitted from Ghana's African Nations Cup squad because he had lost his place in the starting lineup at Dnipro.
Bastia, 13th in Ligue 1, had already reinforced their defence during the January transfer window by signing France international keeper Mickael Landreau and centre back Jacques Faty from Sivasspor.