Welsh was born in Loganholme, south of Brisbane, Queensland, to William Charles Welsh, a sugar manufacture and auctioneer, and Jane (née Porter). At the 1933 state election, he contested the Labor-held seat of Pilbara, whose member Alfred Lamond had retired after three terms. He died on 28 December 1959 in Kalamunda, and was buried in Karrakatta Cemetery.
He won the seat on a 12% swing—despite his party being reduced to a minor party on the floor of Parliament at the same election. He won on a slightly increased margin in 1936, before being defeated in 1939 by Bill Hegney of the Labor Party. He then stood for and won a North Province seat at the 1940 periodic elections for the Legislative Council, which he held for 14 years.
He was a member of the Nationalist Party until 1945, when the party merged into the Liberal Party.
