The International Association of Athletics Federations (IAAF) initially gave Klishina an exemption to compete as a neutral after Russia's track and field squad were banned from Rio following revelations of state-backed doping in the country.
The governing body then withdrew her exemption on Saturday, a source telling Reuters the move was based on new evidence from a World Anti-Doping Agency investigation conducted by lawyer Richard McLaren.
Klishina went to the CAS, which upheld her appeal, and she can now concentrate on long jump qualifying on Tuesday.
"The Court of Arbitration for Sport set aside the IAAF decision and confirmed I am a clean athlete who remains eligible to compete under IAAF rules in the Olympic Games and other international competitions," she said on her Facebook page on Monday.
"With the appeal now behind me I can thankfully focus my time and attention on competing tomorrow night and enjoying my Olympic experience which I have dreamed of since I first began long jumping as a young girl.
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"Thank you, my dearest friends, for all your support. It has meant the world to me over the past few gruelling days."
