Businessman and politician. Baxter was born in Dundee, the grandson of textile entrepreneur William Baxter (1767 - 1854). He was educated at the High School of Dundee and the University of Edinburgh. He was a partner in his father's mercantile company, Edward Baxter & Co. He became a noted international merchant and traveller, publishing several volumes including Impressions of Central and Southern Europe (1850), The Tagus and the Tiber, or Notes of Travel in Portugal, Spain, and Italy (1852) and America and the Americans (1855).
He represented the Montrose Burghs as Liberal Member of Parliament between 1855 and 1885, serving as Secretary to the Admiralty (1868-71) and as Financial Secretary to the Treasury (1871-73).
He died at his home, Kincaldrum House in Angus.
