White voluntarily stood down from the position last month pending an inquiry when he admitted doping after being named in the United States Anti-Doping Agency's dossier on Armstrong.
The 38-year-old was also sacked from his position as elite men's road coordinator at Cycling Australia last month for the same reason.
"Orica-GreenEDGE is a clean team and our commitment to being clean has been a foundation principle of the team since the day of its inception," team owner Gerry Ryan said.
"Professional cycling is at a crossroads. The future of the sport is being determined by what we do today.
"(We) will not step back from taking any necessary decision to protect the integrity of the sport and the team and to restore the confidence of cycling fans around the world."
American Armstrong, who won the Tour de France a record seven times from 1999 to 2005, has been stripped of his titles after being accused of being a central figure in an elaborate doping regime.
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