Nyambui had dropped out of school after primary education. He became a fisherman in Ukerewe District in Mwanza Region, where his potential as a good athlete was spotted by the Region's Athletic Organization. The organization helped in his training and afforded him facilities and guidance in making him a national and international athlete. He also had joined the Tanzania National Service before he went to train as a teacher. He taught school at Bukumbi (20 miles from Mwanza City) before moving to the United States to study for his bachelor's and master's degrees at the University of Texas at El Paso (UTEP). Then he took a contract to train Bahraini athletes along with Canadian coaches Craig Taylor and Greg Peters from 1996-1998. After that he moved back to Tanzania.
Collegiate
He attended UTEP from 1978 to 1982, where, as an older athlete (he was 29 when he graduated), he won four straight NCAA titles in the 10,000 meters, one of only five Division I men to ever accomplish such a feat, and the only Division I man to win four straight indoor 1 mile championships. He also won three straight NCAA titles in the 5,000 meters while at UTEP and was the 1980 NCAA Cross Country champion. In a memorable Millrose Games race in New York in February 1981, Nyambui broke the world indoor 5,000 meter record with a 13:20.4, just ahead of Alberto Salazar who broke the American indoor 5,000 meter record.
* Events before 1906 are considered unofficial. Distances have varied as follows: 2 Miles (1899–1931) and odd numbered years since 2015, 5000 meters (1933–1939), 3 Miles 1932, (1940–1986), and 3000 meters (1987–2014) and even numbered years since 2014
