Suarez was originally banned by Fifa from all football-related activity after biting Giorgio Chiellini during Uruguay's 1-0 win over Italy in a World Cup fixture in Natal in June.
But CAS has made the decision that the Uruguayan should be allowed to return to work, albeit with his playing suspension remaining in place.
The 27-year-old can now train with his new Barcelona team-mates for the first time since his €88 million transfer from Liverpool, while he can also commit to promotional activity.
He is due to return to the playing field on October 26, one day after Barcelona are scheduled to play rivals Real Madrid in La Liga. However, Suarez could well feature in the Clasico as national TV could decide to it to a Sunday fixture.
The extent of Suarez's playing ban was said by CAS to be proportionate with the act committed, with Suarez having twice been caught biting opponents in the past. He was banned for seven matches after biting PSV's Ottman Bakkal while playing for Ajax, then sat out 10 games following a similar incident at Liverpool on Chelsea's Branislav Ivanovic.
He will sit out the first 11 games of Barcelona's season, while his nine-match international ban is still applicable.