The suspended bans will be deferred for a probationary period of three years.
Uefa confirmed Chelsea will be fined £86,000 for the club's failings in the incident.
"The 100,000 euros fine imposed against Chelsea by the Uefa control and disciplinary body remains confirmed (as the club withdrew their appeal), for the improper conduct of their players and the throwing of missiles by their supporters at the match against Barcelona," said a Uefa statement.
"We're happy with the outcome and we've had a fair hearing," said Chelsea lawyer Jim Sturman.
Referee Ovrebo, who also appeared at the hearings, denied several penalty appeals in the match at Stamford Bridge.
And the referee said the post-match incidents were "regrettable and occurred only because of the high emotions and frustrations which arose from the disappointment of a controversial defeat in such an important game."
Ivory Coast forward Drogba, who has also been fined £15,000 by Uefa, will now miss the first three of Chelsea's Champions League games this season while Bosingwa, who was fined £10,000, will miss the first two.
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