The 21-year-old has agreed a three-year deal and arrives at Easter Road on July 1.
Collins told the Hibs website: "We were all very impressed by Yves when he came to Easter Road in January and had hoped he might join us at that point.
"It says much for his qualities that he was on the verge of playing in the Champions League, and I have little doubt that, had he been called upon to do so, he would have done himself justice. It is perhaps to our advantage that he did not play in that game. Had he done so, we might never have had an opportunity to bring him to Easter Road.
"He has benefited from world-class coaching at Chelsea under Silvino Lauro but such is the quality of goalkeepers at Chelsea there was little opportunity for first-team football and at this stage in his career that is what Yves is seeking.
"Yves will continue to develop at our club and have every opportunity to reach his full potential, something that I am confident he will achieve."