"CAS has upheld the appeal by Katusha against the International Cycling Union," the Lausanne-based court said in a statement sent to Reuters.
Katusha, who finished second in the World Tour standings last year, appealed to CAS in December after the UCI rejected their application to compete in the top flight because of the team's doping record over the past four years.
"Following the hearing, the CAS Panel did not reach the same conclusions as the UCI Licensing Commission and decided to uphold the appeal," CAS said.
The decision means Katusha and their world number one Joaquim Rodriguez of Spain can take part in the major cycling races, such as the Tour de France, Giro d'Italia and Tour of Spain, plus several top one-day and one-week races in 2013.
"Undoubtedly, this is one of our biggest victories," said Igor Makarov, president of the Russian Cycling Federation and Katusha boss. "All of us are very happy that justice has finally triumphed."
Rodriguez, who had earlier hinted he might leave Katusha if they could not take part in the major races, greeted the decision with a sigh of relief.
"We're back among the elite and it's great news for the whole team," said the Spaniard, who is competing in the Tour of Oman this week. "As for myself, it gives me added confidence to look ahead and make plans for the rest of the season."
With the current campaign having already started, the UCI is in an uncomfortable position because only 18 teams are allowed in the World Tour.
"The UCI will now evaluate the consequences of this ruling and will communicate further in coming days, as soon as such evaluation has taken place," the sport's governing body said in a statement.
In rejecting Katusha's original application, the UCI's licence commission said the Russian outfit have had the most doping cases among all the Pro Tour teams, citing four cases between 2009 and 2012.
One such case involved Katusha's top sprinter Denis Galimzyanov, who tested positive for the banned blood booster EPO last April.
Katusha general manager Vyacheslav Ekimov has flatly denied the allegations.
"The UCI said Katusha don't do enough tests within the team to catch doping cheats," he told reporters in December.
"They also blamed us for Galimzyanov's positive test, even though the rider had admitted that it was his own mistake."
Ekimov, a long-time team mate of disgraced American cyclist Lance Armstrong, also denied any personal involvement in doping.
"During the hearing, the UCI never mentioned my name, (Katusha leader) Denis Menchov or (Italian doctor) Michele Ferrari," triple Olympic champion Ekimov said at the time.
Menchov came under a cloud in 2011 when French sports daily L'Equipe produced its doping suspicion index, in which riders were rated on a scale from 0 - not suspicious - to 10 - highly suspicious. Menchov was rated at 9.
The Russian rejected the allegations and said it was just a case of sour grapes from the French.
Ferrari was banned from cycling for life for his alleged ties to Armstrong, helping him win a record seven Tour de France titles on the back of a highly sophisticated doping scheme.