William Arthur Neilson AC (27 August 1925 – 9 November 1989) was Premier of Tasmania from 1975 to 1977.

Born in Hobart, and educated at Ogilvie High School, Neilson became a postman before entering politics.

Neilson was elected to the Tasmanian House of Assembly on 23 November 1946 at the age of 21, representing the Labor Party (ALP).

The following year Neilson's government was re-elected, narrowly defeating (by just one seat) the Liberal Party led by Sir Max Bingham; but towards the end of his tenure, he suffered from nervous exhaustion.

After his term as premier, Neilson accepted the position as Agent-General for Tasmania in London, but soon his successor in the premiership, Doug Lowe, abolished the post on cost-cutting grounds.