The move is the 20th transfer between the French team and the Blues since both clubs came under the ownership of BlueCo.
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The agreement includes a buyback clause and is expected to be followed by more business between the sides this week.
Chelsea striker Deivid Washington is also set to join Strasbourg, while either Dario Essugo or Mykhailo Mudryk could move to France on loan.
20-year-old Kellyman joined Chelsea from Aston Villa for £19m in 2024 but struggled with hamstring injuries and never made a senior appearance.
He impressed during a loan spell at Cardiff City last season, helping them win promotion to the Championship.