The striker moves to MLS club Chicago Fire for a fee of €2m.
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Bamba said: "The direction the team is taking, both on and off the field, is very exciting and I hope to contribute to its future successes.
"I am ready for this new challenge and I can't wait to work with my new coaches and teammates with the aim of achieving great things together."
Celta youngster Luca de la Torre has also moved to MLS on-loan to San Diego FC.
And last week, Argentine striker Tadeo Allende joined on loan Inter Miami. All three transfers had the approval of Celta coach Claudio Giráldez.