CAS said in a statement that it had removed the clause which banned the 27-year-old from "any football-related activity" following an appeal by the Uruguayan Football Association (AUF) on Suarez's behalf.
The Barca player remains ineligible to play in official matches during the four-month period, and his nine-game international ban also stays in force following the notorious incident during the World Cup group game on June 24 which Uruguay won 1-0.
However, a spokesman for soccer's world governing body FIFA said he could play in friendly internationals for club and country. This could allow him to make his Barcelona debut against Mexican side Leon on Monday if selected.
"The sanctions imposed on the player by FIFA have been generally confirmed," CAS said in a statement. "However, the 4-month suspension will apply to official matches only and no longer to other football-related activities (such as training, promotional activities and administrative matters)."
"It has however considered that the stadium ban and the ban from "any football-related activity" were excessive given that such measures are not appropriate to sanction the offence committed by the player and would still have an impact on his activity after the end of the suspension."
Suarez's legal team said they had successfully argued that FIFA had misapplied its own rules when considering the case and the sanction it imposed on other football-related activities was disproportionate.
"As a result, Suarez is now permitted to train and attend matches with his Barcelona team mates in preparation for the new season," his lawyers said in a statement.
Barcelona said in a statement that the forward would train with the La Liga club on Friday and will be presented as a Barca player at the Nou Camp on Monday when they play Leon.
"I expected something different, although not much," said AUF president Wilmar Valdez in a statement.
"CAS is a totally independent tribunal and this is to do with the way people see things, it's a cultural matter. The way we live football in South America is different to Europe.
"For us there are things which are normal and which deserve sanctions, but not such harsh ones.
"The training is something positive because not being able to train was too tough.
"It was shown in the World Cup, in the matches Suarez did not play in, that he is a fundamental player. We will have to work to look for the appropriate alternatives."
AUF lawyer Daniel Cravo told Sky Sports News: "We don't think it was the worst behaviour of a player in a World Cup. We have seen worse situations and the players haven't been sanctioned in that level."
Uruguay and Italy were drawing 0-0 when the incident happened late in the game. Shortly afterwards, Diego Godin headed the winner from a corner to send the South Americans into the last 16 at Italy's expense.
Suarez went to CAS, which conducted a hearing on the matter last Friday, after losing a first appeal at FIFA.
A Liverpool player at the time of the biting incident, Suarez has since joined Barcelona for a fee reported to be 81 million euros ($108.5 million) by local media.
Banned twice before for biting, Suarez initially denied sinking his teeth into Chiellini but photographs of marks on the Italian defender's shoulder were damning.
Suarez initially claimed that he had been the victim, falling to the ground and clutching his teeth after the players clashed.
He eventually accepted responsibility and apologised for the incident one week later, days after FIFA had imposed the ban.
"The truth is that my colleague Giorgio Chiellini suffered the physical result of a bite in the collision he suffered with me," Suarez said in a statement on Twitter.
"For this: I deeply regret what happened; I apologise to Giorgio Chiellini and the entire football family; I vow to the public that there will never again be another incident like (that)," he added
FIFA later explained Suarez was given a heavy punishment partly because he had twice before been banned for biting and because he had shown no remorse at the time.
Despite widespread condemnation of his actions, general reaction to the ban itself was mixed. It prompted fury in his South American homeland, where he was given a hero's welcome on his return from Brazil during the World Cup.
Chiellini himself said the ban was excessive and world players' union FIFPro said Suarez had been "trialled and vilified in public".
FIFPro suggested that part of the ban should be made conditional and should include an obligation for Suarez to seek treatment.
The ban means he will not be able to make his Barcelona debut until the end of October. He will also miss next year's Copa America in Chile, when Uruguay have their next competitive matches.
Uruguay will play a minimum of three and maximum of six matches at the Copa, meaning Suarez will also miss between two and five matches of the 2018 World Cup qualifying campaign.
The forward could make his Barca debut at Real Madrid in El Clasico with the match scheduled for the weekend of Oct. 25-26. However, Suarez would only be able to play if the game went ahead on the 26th, the day after his suspension ends.
($1 = 0.7467 Euros)