Baker was first elected to the House of Commons in the 1974 election as the Liberal Member of Parliament (MP) for Gander—Twillingate, in Newfoundland and Labrador. He was re-elected in every subsequent election (representing Gander—Grand Falls after 1988) until his appointment to the Senate by Governor General Adrienne Clarkson, on the recommendation of Prime Minister Jean Chrétien, in 2002.
Although a popular and articulate MP, he was hurt by the tradition of appointing no more than one Canadian Cabinet minister from Newfoundland at a time, and by his reputation as a maverick who said what he thought rather than what the party leadership would like him to say. Fred Mifflin's and Brian Tobin's appointments to cabinet following the 1993 election meant Baker had to remain on the backbench. Tobin's resignation from the cabinet to become Premier of Newfoundland and Labrador opened the way for Baker to be appointed as Minister of Veterans Affairs. But when Prime Minister Chrétien lured Tobin back to Ottawa for the 2000 election, Baker was removed from Cabinet. He was appointed to the Senate in 2002.
Baker lives in Gander, Newfoundland and Labrador, with his wife Averill Baker.