Anthony van Buren was born in New Zealand in 1966 and grew up in Christchurch. He started playing the violin at the age of 10, but switched to the viola three years later. Anthony van Buren obtained his Bachelor of Arts degree in History from Canterbury University in 1986. He then continued at Canterbury to study violist full-time, followed by six months as violist in the New Zealand Symphony Orchestra.

In 1989 he left New Zealand to study further at Rice University in Houston, Texas with the world famous Israeli violist Atar Arad. He completed his Master of Music degree in 1991, but continued his studies with Atar Arad and accompanied him to Indiana University in Bloomington, Indiana.

In 1992, Anthony van Buren literally stumbled upon the job in Sønderjylland's Symphony Orchestra and moved to Denmark in January 1993.

For periods during 2001 and throughout 2002, Anthony van Buren lived in Las Palmas in the Canary Islands, where he worked as solo viola player in the Orquesta Filarmonica de Gran Canaria.