The judgement by the Court of Arbitration for Sport was due on Monday afternoon but Sky has learned that the court has ruled against the British Olympic Association.
It has decided that the association's lifetime ban on drug cheats is not compatible with the World Anti-Doping Agency's code and is therefore unenforceable.
Cyclist Millar and sprinter Chambers, who have both admitted cheating with drugs, will be eligible to compete for Team GB at the Games.
They both received a two-year ban for their doping offences, Chambers in 2003 and Millar in 2004.
Prior to this case, British athletes who were found guilty of doping were subjected by the BOA to a lifetime ban from the Olympics. This differed from other countries' approach to drug cheats and the case was taken to CAS for a ruling.
The BOA had argued that its lifetime ban for drug cheats was a "selection policy" and not a double sanction for cheats.
In November, in a case brought by American athlete LaShawn Merritt, CAS ruled that the International Olympic Committee's 'rule 45' which banned all athletes worldwide from an Olympic Games was illegal.
The latest decision appears to have backed up that ruling.
The BOA and Dwain Chambers said they would give their reaction on Monday.
Following the news, British Hurdler Andy Turner tweeted: "Either make a lifetime ban for drug cheats worldwide or scrap it completely.
"The world won't follow Britain's rules so I'm happy for Dwain. I know my opinion will annoy people but I don't care. I see convicted drug cheats on the world stage all the time."