He was born in Chelsea, England, the son of a Scottish novelist and colonizer, John Galt, by his wife Elizabeth, only daughter of Alexander Tilloch. He was a first cousin of Sir Hugh Allan of Montreal.
He was a member of the Great Coalition government in the Province of Canada that secured Confederation between 1864 and 1867. He became a leading figure in the creation of the Coalition when he was asked to become premier of the Province of Canada by then Governor General Sir Edmund Walker Head. Doubting his own ability to demand the loyalty of the majority of members of the Legislative Assembly, he turned down the position, but recommended that George-Étienne Cartier and John A. Macdonald be asked to become co-leaders of the new government.
In return, Cartier and Macdonald asked him to become Inspector-General of Canada. He accepted the post on the condition that Macdonald and Cartier made Confederation a key platform in their new government. In 1858, Alexander Tilloch Galt made a motion in the Legislature at Kingston recommending that the Province of Canada ask the British Government to create a federal union of British North America (Canada East and West, Prince Edward Island, Newfoundland, New Brunswick, and Nova Scotia) and Rupert's Land (owned by the Hudson's Bay Company). The motion succeeded, and Alexander Galt, John Ross, and Sir George-Étienne Cartier went to London to begin the long process of convincing the British to make British North America into the first sovereign Dominion within the British Empire.
As Inspector General, Galt reformed the Province of Canada's banking system trade policies. He was the main architect of the Cayley-Galt Tariff, which protected colonial businesses and caused consternation in both Britain and the United States.
July 1, 1867, Canada East and West, New Brunswick, and Nova Scotia became the first provinces in British North America to form the Dominion of Canada. Galt served as the first Minister of Finance in the new confederation. As minister of Finance, he reversed many of his earlier policies, promoting trade within the British Empire. Following a strong disagreement with Macdonald and Cartier concerning the fate of the Commercial Bank of Canada, Galt resigned from government. He continued to sit as an MP until 1872.
Nevertheless, Galt remained an important figure in Canadian business and politics. In 1877, The British appointed him as their representative in the Halifax Fisheries Commission concerning American fishing rights in Canadian waters. Following a rapprochement with the re-elected Macdonald, Galt was sent to London to be Canada's informal representative there. As this was the only important office of the Canadian government overseas at the time, he also travelled to France and Spain to negotiate trade deals with those nations. The British government knew of these trips and was not pleased that Canada had developed a foreign policy separate from the Empire. The British demanded that Galt's position be formalized, and in late 1880, he became the first Canadian High Commissioner in London. He left his post on 1 June 1883.
On February 9, 1848, Galt married Elliott Torrance, the daughter of John Torrance, of Saint-Antoine Hall, Montreal. She died on May 25, 1850, shortly after giving birth to their only son, Elliott. Later he married her younger sister, Amy Gordon Torrance. Amy gave birth to 7 daughters and 2 more sons. They lived in Montreal at their house within the Golden Square Mile, which Galt built in about 1860. Galt appears to have had a very non-sectarian approach to religious faith and although the grandson of a Calvinist theologian, Alexander Galt supported both the Methodist and Anglican churches while his wife, Amy, was a lifelong Presbyterian.
Sir Alexander Galt and his son Elliott Torrance Galt co-founded the city of Lethbridge, Alberta in 1883, when he established a coal mine on the banks of the Oldman River in the southwest portion of the District of Alberta, Northwest Territories. The Canadian Post Office refused to accept the name Lethbridge for the community in the Dominion of Canada. Sir ed to the prairie level from the river valley. Canada's Governor General, the Marquess of Landsdowne, demonstrated the Dominion government's support of the Galt enterprises, by opening the Galts' railway in September 1885 in Lethbridge.
Galt's company, the North Western Coal and Navigation Company went through a variety of name changes as it moved into railways, and irrigation enterprises. Prime Minister Sir Wilfrid Laurier dedicated the Galt Hospital addition, which houses the Galt Museum, in 1910.
Galt is interred in the Mount Royal Cemetery in Montreal, Quebec. He has a street named after him: Avenue Galt in the borough of Verdun, Quebec, in the city of Montreal where he had lands. In Lennoxville, Quebec, the Alexander Galt High School was named in his honour.
The Galt Gardens public park and Galt Museum (formerly a hospital) in Lethbridge are named after him.
Galt was the founding president of The Guarantee Company of North America in 1872, providing fidelity bonds to guarantee the surety of employees of railroads and government. The company still exists today as the largest provider of surety bonds in all of Canada in public works and government services.
Galt was portrayed by Patrick McKenna in the 2011 CBC Television film John A.: Birth of a Country.