The triple Olympic gold medal winner failed to make the team in both the marathon and the 10,000 metres.
Bekele had appealed a decision to leave him out of the marathon team due to a lack of race time, while his hopes of running the 10,000 metres in Rio were effectively dashed when he failed to finish a race in Hengelo, which doubled up as an Olympic trial.
The Ethiopian Athletics Federation said in a statement it had picked former world champion Ibrahim Jeilan, 2012 World Junior champion Yigrem Demelash, Tamirat Tola and Abadi Hadis for the 10,000 metres in Rio.
Bekele, who won gold in the 10,000 metres at the Athens Olympics in 2004, and in the 5,000 and 10,000 metres in Beijing four years later, was left out of the marathon team having not run enough big races over the past year.
Ethiopia's squad will include 2016 Tokyo marathon winner Feyisa Lilesa and 2015 Boston champion Lelisa Desisa, as well as Lemi Berhanu and Tesfaye Abera.
Ethiopia's preparation for the Games, which begin on Aug. 5, was disrupted by concerns over their drug-testing systems, after the IAAF governing body said in March that it was one of five countries that were in "critical care".
The east African nation, which alongside neighbour Kenya has for many years dominated distance running on the track and roads, subsequently announced that it would carry out doping tests on up to 200 athletes.
The Ethiopian Athletics Federation last week banned two athletes, Taemo Shumye and Sentayehu Merga, for four years after they tested positive for banned substances.
The federation said four other athletes remain under investigation by the World Anti-Doping Agency and the IAAF for doping.
(Editing by George Obulutsa and Toby Davis)
