"It is a hollow victory for WADA (World Anti-Doping Agency)," BOA chairman Colin Moynihan said. "We live in difficult days when WADA spends time and money reducing the powers of countries taking stands against doping in sport, such as ourselves, New Zealand and Canada.
"On the decision made now by CAS, athletes such as David Millar and Dwain Chambers will be eligible for selection for the Olympic Games.
"So long as they meet the eligibility criteria they will be selected by Team GB.
"If they become eligible for selection by Team GB they will be treated as all other team members. There will be no two-tier membership for Team GB."
Moynihan had claimed he was 'cautiously optimistic' after a hearing in London last month but the three-strong panel of sport's highest legal authority ruled that their position was contrary to the binding World Anti-Doping Agency code, to which they are a signatory.
Canadian Richard McLaren, Switzerland's Michele Bernasconi and American David W. Rivkin claimed that the BOA's unique and hardline stance amounted to a double sanction and dismissed their claim that the Olympic Charter gave them the right to select whoever they liked for their Olympic team.
The judgement was formally posted on the CAS website just before 3pm - but the result had already been widely reported and the BOA, who received the verdict over the weekend, will give their first response in a news conference scheduled for later today.
CAS claimed the precedent for their decision was set last year when the International Olympic Committee were told their 'Osaka rule', which prevented athletes found guilty of a serious doping offence from competing at the Games that followed their suspension, was illegal.
"The CAS panel has ruled that the BOA bye-law related to the selection of British athletes for the Olympic Games was not in compliance with the World Anti-Doping Code," read a CAS statement.
"Such decision confirms the jurisprudence established last year in the case between the US Olympic Committee and the International Olympic Committee."
Chambers made his Olympic debut in Sydney 12 years ago but was suspended for the Athens Games after testing positive for THG in 2003. After returning to the sport in 2005, he challenged the BOA's ruling in the High Court in the build-up to Beijing but lost his case.
In the past three years he has been Britain's undisputed number one sprinter, winning the world indoor title in 2010 and claiming silver at that year's European Championships in Barcelona.
Millar admitted to using blood doping in the days before the Athens Olympics, where he was strongly tipped for a medal in cycling's road time trial. Since returning to the sport, after a two-year ban ended in 2006, he has become a passionate campaigner for anti-doping and even sits on WADA's athletes' commission.
He played a vital role in helping Mark Cavendish win road race gold at last year's World Championships in Copenhagen and could also challenge British team-mate Bradley Wiggins for a medal in the road time trial. However, he has previously said he has no wish to be the 'black sheep' of the team and may not put himself forward for selection.
However, British Cycling performance director Dave Brailsford has insisted he wants to pick the best team at his disposal - and that must surely include Millar.
"Our team for the Games is being selected in June and across all disciplines we’ll pick the team based on which riders are fit and available, and who we believe have the best chance to deliver medals," said British Cycling, in a statement issued just after the verdict went online.
"Ahead of that we won’t be speculating on who may or may not be selected."
The ban does not just apply to athletes but also coaches, which means Linford Christie, who won the Olympic 100m title in 1992 but tested positive for nandrolone towards the end of his career, could now receive official accreditation to assist with his stable of sprinters if he is nominated by UK Athletics.