The Sixteenth Karmapa instructed Kyabje Tulku Urgyen Rinpoche to found a monastery in Nepal. Tulku Urgyen obeyed, taking his wife Kunsang Dechen and two sons, Chökyi Nyima Rinpoche and Chokling Rinpoche. Construction began in 1972, and the monastery was dedicated in 1976. HM King Birendra attended. Tulku Urgyen died on February 13, 1996, whereupon his son Chokyi Nyima succeeded him as abbot (his brother becoming "vajra master"). Today the monastery boasts about 180 monks and 108 nuns at an affiliated nunnery, Nagi Gompa (some distance away).
In 1981 the monastery established the Rangjung Yeshe Institute (or Shedra Institute), a multi-year course in Tibetan language and Buddhist philosophy designed for Western dharma students. It has since entered into a cooperation agreement with Kathmandu University to form the Center for Buddhist Studies whereby its students can be awarded BA and MA degrees from KU, with a major in "Buddhist Studies with Himalayan Language."
Moran, Peter. Buddhism Observed: Travelers, Exiles, and Tibetan Dharma in Kathmandu. RoutledgeCurzon, 2004. An anthropological/sociological look at "Western" Buddhist tourists/pilgrims to Boudhanath. Ka-Nying Shedrup Ling is mentioned periodically throughout the text (along with several other area monasteries) and especially the section beginning on page 74.