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Weller was born in Vienna, Austria, where he studied at the Vienna Hochschule für Musik and first gained renown as a prodigy on the violin. His father, also named Walter Weller, was a violinist in the Vienna Philharmonic. At age 17, Weller became a member of both the Vienna Philharmonic and the Vienna State Opera Orchestras. In 1961, at age 22, he became joint concertmaster of the Vienna Philharmonic with Willi Boskovsky, and remained in this post for 11 years.
Weller’s first engagements as a conductor were in 1966, deputising at short notice for Karl Böhm. His conducting debut at the Vienna State Opera was in 1969, leading Die Entführung aus dem Serail. He later served as Generalmusikdirektor (GMD) of Duisburg, Germany, for the 1971-1972 season. From 1975 to 1978, he was principal conductor of the Niederösterreichischen Tonkünstlerorchester. From 1994 to 1997, he was Chief Conductor of the Basel Symphony Orchestra, the last conductor with that title before the orchestra joined with the Radio Symphony Orchestra Basel to form the Sinfonieorchester Basel, and in parallel, was GMD in Basel. He also served as principal guest conductor of the Spanish National Orchestra from 1987 until 2002. Weller served as Music Director of the National Orchestra of Belgium from 2007 to 2012, at which time he became Honorary Conductor of the orchestra. In 2010, he became the first honorary conductor of the Trondheim Symphony Orchestra. He also became Conductor Laureate of the Stuttgart Philharmonic Orchestra and Associate Director of the Valencia Orchestra.
In Great Britain, Weller held several principal conductorships. From 1977 to 1980, he was principal conductor of the Royal Liverpool Philharmonic. He then held the same post with the Royal Philharmonic Orchestra from 1980 to 1986. In 1992, he became principal conductor of the Scottish National Orchestra, and helped to mediate strained relations between the orchestra's musicians and management at the time. He served as the SNO's principal conductor until 1997, and subsequently became the orchestra's Conductor Emeritus. The Bank of Scotland honoured Weller by printing his portrait on a special 50 pound note.
His widow and son survive him.
The Weller Quartet's recordings for Decca Records included Haydn’s complete Op 33, Mozart, Beethoven, Brahms, Berg and Shostakovich. Weller's recording début as a conductor was with the Suisse Romande Orchestra, in Shostakovich's Symphony No. 1 and Symphony No. 9. His recordings of the Beethoven, Mendelssohn and Prokofiev symphony cycles have long remained available on LP and CD.
Weller collected many prizes and awards, including the Grand Decoration of Honour in Silver for services to the Republic of Austria, bestowed on him in 1998.
- Conrad Wilson (17 June 2015). "Walter Weller". The Herald. Retrieved 17 June 2015.
- "Wiener Dirigent Walter Weller 75-jährig gestorben". Kurier. 17 June 2015. Retrieved 17 June 2015.
- Who’s Who, London: A & C Black
- Bigler-Marschall, Ingrid (ed.), Deutsches Theater-Lexikon, Band VI, Faszikel 32/33 (Weisbrod - Wiel). De Gruyter Saur (ISBN 978-3908255475), pp 3196-3197 (2006).
- "Top Russian conductor Andrey Boreyko to be Music Director of the NOB from 2012-13" (Press release). National Orchestra of Belgium. 21 September 2010. Retrieved 23 December 2010.
- "Ex-RSNO principal Walter Weller dies aged 75". The Herald. 15 June 2015. Retrieved 17 June 2015.
- "Conductor and violinist Walter Weller has died". Gramophone. 16 June 2015. Retrieved 17 June 2015.
- "Reply to a parliamentary question about the Decoration of Honour" (PDF) (in German). November 2012. Archived from the original (PDF) on 6 October 2014.
- The Gramophone, February 1973