CAS also said on Friday Chinese swimmer Chen Xinyi was provisionally suspended.
Tomasz, who like his brother, was down to compete in the 94kg category, tested positive for performance-boosting anabolic steroids.
"The athlete is declared ineligible to compete in and is excluded from the Olympic Games," CAS said. "His accreditation shall be withdrawn."
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Earlier on Friday the Polish Anti-Doping Agency said Adrian, an Olympic champion in weightlifting four years ago in London, had also been sent home after testing positive for nandrolone.
Adrian failed a test in Poland before the Games, Michal Rynkowski, director of Poland's Commission Against Doping in Sport, told reporters in Warsaw.
"I can clearly confirm that a urine sample taken from Adrian Zielinski gave a positive result for nandrolone. Its concentration was nearly twice the permissible norm," he said.
"Today we have received confirmation. The athlete faces a four-year suspension."
Adrian won gold in the 85kg category in London and had moved up to the next weight category, 94kg, for Rio.
Chen finished fourth in the women's 100m butterfly final on Sunday and was scheduled to swim in the 50 freestyle heats on Friday in Rio. She tested positive for hydrochlorothiazide, CAS said.
"The athlete accepted a provisional suspension on a voluntary basis," CAS said. "The procedure will continue and the CAS ... will issue a final award before the end of the Games."
CAS also confirmed the disqualification of Bulgarian runner Silvia Danekova who tested positive for blood-boosting EPO.
The 33-year-old, who was due to compete in the women's 3000m steeplechase on Monday, has been suspended after failing an out-of-competition test on Aug. 1, the Bulgarian Olympic Committee (BOC) has said.
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