The oil, Boats making a dash for Whitby Harbour in a Storm, joins four other paintings by the artist in the Scarborough collections.
The gallery was keen to secure the latest work depicting a Whitby seascape as most of its other sea scenes are of Scarborough.
Karen Snowden, head of collections, said: “We wanted Boats making a dash because we already have several paintings by Roe and this one complements them.
“The Scarborough Art Gallery collection reflects the whole of the borough, not just the town of Scarborough.
“At present, we only have watercolours of Whitby and this is an oil.”
Born in London, Roe was the son of animal painter Robert Henry Roe.
He specialised in Yorkshire coastal scenes and lived and worked in Scarborough in a studio on Huntriss Row from about 1868 to 1880.
The painting was previously owned by a Finnish collector.
It cost £11,000 in total, with £5,000 coming from The Art Fund, £1,500 from the Friends of Scarborough Art Gallery, £4,400 from a bequest fund held by Scarborough Borough Council and £100 from public donations at the gallery.