Sellar was the son of Patrick Sellar of Westfield, Morayshire, a lawyer, factor and sheep farmer, and his wife Ann (née Craig).
He was educated at Rugby School, and at Balliol College, Oxford where he was a favoured student of Benjamin Jowett.
In 1882 he was elected Member of Parliament for Haddington Burghs until the constituency was merged in the Redistribution of Seats Act 1885.
In 1885 he was elected MP for Partick which he held until his death at the age of 54 in 1890.
This article about a Liberal Member of the Parliament of the United Kingdom representing a Scottish constituency is a stub.