Bruyneel was banned for 10 years, while Celaya and Marti got eight-year bans after the decision by the American Arbitration Association North American Court of Arbitration for Sport (AAA), USADA said in a statement.
The trio all worked for Armstrong's U.S. Postal Service team (USPS), which changed its name to Discovery Channel after a change of sponsors in 2005, and opted for arbitration when the charges were originally levelled against them in June 2012.
"The evidence establishes conclusively that Mr. Bruyneel was at the apex of a conspiracy to commit widespread doping on the USPS and Discovery Channel teams spanning many years and many riders," said the statement.
"Similarly, Dr. Celaya and Mr. Marti were part of, or at least allowed themselves to be used as instruments of, that conspiracy."
American Armstrong was stripped of his seven Tour de France titles and given a lifetime ban for doping in 2012, finally admitting his use of banned substances in a TV interview with Oprah Winfrey in January 2013.
Two other doctors connected to the team, Spaniard Luis Garcia del Moral and Italian Michele Ferrari, were handed lifetime bans from professional sport by USADA in July 2012.
USADA's 2012 report said the USPS team had run "the most sophisticated, professionalised and successful doping programme the sport has ever seen".
Belgian Bruyneel is a former professional cyclist who was team manager for all of Armstrong's seven Tour de France wins from 1999 to 2005.
Often described as Armstrong's right-hand man, Bruyneel enjoyed further success with Astana in 2008-9 before moving to run the RadioShack team, a position he resigned from when USADA published its report into Armstrong's doping.
"I do not dispute that there are certain elements of my career that I wish had been different, nor do I dispute that doping was a fact of life in the peloton for a considerable period of time," the 49-year-old said in a statement on his website (www.johanbruyneel.com).
"However, a very small minority of us has been used as scapegoats for an entire generation. There is clearly something wrong with a system that allows only six individuals to be punished as retribution for the sins of an era."
Bruyneel, who did not give evidence in the arbitration hearings in London in December, said he continued to dispute USADA's jurisdiction over him and might still appeal to the Court of Arbitration for Sport (CAS).
Pedro Celaya was USPS doctor from 1997 to 1999 before being replaced by fellow Spaniard Del Moral. He returned to the team in 2004.
"The panel found that Dr. Celaya possessed and administered doping products, including EPO, blood transfusions, and cortisone," the statement said.
Spaniard Marti, who also refused to testify in front of the three-member arbitration panel, was a trainer for the team from 1999 to 2007 before going on to work under Bruyneel at Astana.
He was accused by USADA of delivering banned substances "including EPO, testosterone, human growth hormone and cortisone" from Valencia to riders around the world and assisting with the use of them.
The AAA panel "confirmed that" USADA had the authority to bring the cases because it had discovered the violations, USADA's statement said.
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