Feiler was born in Tel Aviv in 1951 to Eliezer and Pnina Feiler, and moved with his family to kibbutz Yad Hana in 1967. His father, Eliezer Feiler, was a left-wing activist. In 1978, he and others secretly met with a group of Palestine Liberation Organization representatives in Bucharest while it was still illegal. Eliezer Feiler was tried and eventually sentenced to six months of community service and a 4,000 Israeli lira fine. The fine was paid, but the sentence was never served because, while the legal process was ongoing, the law had changed and it was no longer illegal to meet with members of the PLO. His mother, Pnina Feiler, born 1923, was among the founders of Yad Hana. She worked with mobile health centrals in Palestinian villages in the West Bank that have to travel far to get access to health-care and other services until 2015, when she stopped due to her advanced age. Dror Feiler served as a paratrooper in the Israel Defense Forces.
In 1973, Feiler immigrated to Sweden. He renounced his Israeli citizenship, as it was then a condition for gaining Swedish citizenship. Feiler studied new music and its interpretation at the Fylkingen Institut for New Music from 1975 to 1977, musicology at Stockholm University from 1977 to 1978 and composition at the Music Academy of Stockholm from 1978 to 1983.
Feiler also plays saxophone in the jazz band Lokomotiv Konkret, and founded the Too Much Too Soon Orchestra. In January 2004 he and Gunilla Sköld-Feiler made international news with their art installation Snow White and The Madness of Truth, which referred to female suicide bomber Hanadi Jaradat, which was vandalised by the then Israeli ambassador to Sweden Zvi Mazel. The installation consisted of a long pool of water coloured blood red, upon which floated a small white boat named "Snövit" ("Snow White") carrying a portrait of Hanadi Jaradat. She had blown herself up in October 2003 in an attack on Maxim's restaurant in the northern Israeli city of Haifa, killing 21 people and injuring 51.
Feiler is now the chairman of the Swedish organization Jews for Israeli-Palestinian Peace (JIPF) and the European organization European Jews for a Just Peace (EJJP). He is also a member of the editorial board of the New Colombia News Agency (ANNCOL).
He runs the artspace TEGEN 2 in Stockholm together with Gunilla Sköld Feiler.
He is active as a composer of modern music, which includes composition music for symphonic orchestras, opera, chamber music and electro-acoustic music. In April 2008, the Bavarian Radio Symphony Orchestra dropped the world premiere of his composition Halat Hisar (State of Siege), after musicians complained that the music, which includes machine gun sounds, was so loud that it gave them ear problems and headaches.
On 31 May 2010 Feiler was aboard one of the ships involved in the Gaza flotilla raid and sustained some minor injuries to the face during the raid. For his participation in the raid, Feiler was banned from entering Israel for 10 years. In July 2010, he flew to Israel together with Swedish MP Mehmet Kaplan, who had also received a 10-year entry ban over his participation in the Gaza flotilla, planning to lodge a complaint with the Israel Police over the flotilla raid. They were refused entry at Ben Gurion Airport and deported. In 2011, Feiler was involved in the Freedom Flotilla II, and was among the 15 activists arrested by Israeli authorities aboard the boat Dignité. He was subsequently deported from Israel. 
In 2013, Feiler appealed this ban in order to visit his ailing 90-year-old mother.
In the 2010 Swedish general election, Feiler was a candidate for the Left Party (Swedish: Vänsterpartiet) in Stockholm. He obtained 1,784 personal preference votes in Stockholm Municipality (4.51% of the Left Party votes, the second most voted candidate on the list after party chairman Lars Ohly) and 629 personal preference votes in Stockholm County (1.99% of the Left Party votes).
Feiler took part in Freedom Flotilla III, aboard the Swedish vessel Marianne. The ship was intercepted by the Israeli Navy on June 29, and Feiler was arrested.