Linn was the son of Erik Johan Sjödahl, chief inspector of ironworks at Billnäs Bruk, and his wife, the former Engla Gustava Collin. The family was of Swedish descent and lived near Pojo, on the southwestern coast of Finland, which was then a part of the Kingdom of Sweden. Young Carl displayed an early affinity for seafaring when. At age thirteen, after a great fire destroyed most of his school, the Imperial Academy in Turku, Sjödahl made for Helsingfors and there boarded a ship sailing for America. When the crew discovered him, he was put to work as a cabin boy until he could be returned home. During the voyage he began to learn English from the other sailors.
In April 1830 he returned to the sea as part of the crew of a merchant ship. Over the next decade he made the Atlantic crossing fifty-three times and completed three full circuits of the globe. On June 13, 1833 he registered as an immigrant to the United States in New York City.
Sjödahl apprenticed as a maker of matches and pursued that trade in New York, Savannah, and New Orleans. There he accumulated enough capital to purchase a packful of tinware which he set off to peddle inland. He worked his way as far as Montgomery by 1838 and he resumed making and selling matches while sleeping on cotton bales at the riverside. After a while he partnered with Thomas Joseph in the fruit business. He continued to make matches to sell at their stand, even after it expanded with a bakery. To make it easier to do business, Sjödahl petitioned the state legislature to change his name to "Carl Linn", which was further Anglicized to "Charles".
Linn opened a mercantile business which flourished and made him a wealthy businessman. Finally ready to settle down, he purchased a large farm. He then voyaged home to Finland and married his childhood sweetheart, the former Emelie Antoinette Forss at Koskis on September 5, 1842, and brought her to Alabama as his wife. They had four children: Elvina Charlotte ("Ellen"), Charles Washington, Antoinette "Annie" Aurelia, and Edward. Emelie died in Montgomery from complications with Edward's birth on February 16, 1852.
Linn did not remain long without a helpmate. On December 28 of the same year he married the former Eliza Jane Summerlin of Montgomery. Over the next decade she bore him four more children: Mary Eliza, Lizzie Jane, George Thomas and George Marion. At the outbreak of the Civil War he sent all but his oldest son, Charles William, to Dresden for their safety.
Linn and Charles William volunteered their services to the Confederate Navy and were posted to the Kate Dale, a fast sloop which ferried cotton through the Union blockades to trade in Great Britain and Cuba for gold and badly-needed supplies. After many successful crossings, the ship was finally captured off the Florida keys and Linn and his son were taken prisoner and sent to Washington to stand trial as war criminals. They were both pardoned, however, and the two Linns joined the wholesale grocery firm of Flash, Lewis & Co. in New Orleans, recruiting fellow Finns from the docks as workers.
After Charles William's death in 1871, Linn sold his share in the New Orleans firm and rejoined the rest of his family at the farm in Montgomery. Not long afterward James Powell and other investors in the Elyton Land Company interested him in the idea of opening a bank in the newly-founded City of Birmingham. He agreed and launched the National Bank of Birmingham in 1872 with $50,000 in gold. It was the first bank in the city, and the first in Northern Alabama chartered under the National Bank Act.
In 1873 Linn was elected to the Birmingham Board of Aldermen to serve in Mayor James Powell's administration. Later that year, Linn erected the monumental 3-story National Bank of Birmingham building on the corner of 1st Avenue North and 20th Street at a time when the city's future was doubtful. The building became known as Linn's Folly, and it was there that Linn hosted the legendary New Year's Eve Calico Ball that signaled the city's emergence from a cholera epidemic and the nationwide financial panic.
In 1874 Linn created a small park in a half-block behind the Relay House. Linn extended his investments from banking to industry, organizing two of the city's first such major manufacturing ventures, the Linn Iron Works and the Birmingham Car and Foundry Company with skilled workers brought in from Cleveland and Cincinnati. Linn purchased some of his equipment from the Confederate Iron Works in Selma.
Eliza Jane died on February 10, 1875 and Linn married the former Fannie H. Clark on August 24 of the same year. On Saturday June 11, 1881 he hosted a celebration of his 67th birthday at Linn's Park with bands, ice cream, and speeches. The day was also marked by an eclipse of the moon. He died a little over a year later, in August 1882.
Before his death Linn issued a bold proclamation which was inscribed on his mortuary in Oak Hill Cemetery:
I shall have my tomb built upon a high promontory above the town of Birmingham, in which you men profess to have so little faith, so that I may walk out on Judgment Day and view the greatest industrial city of the entire South.
Downtown's Linn Park was re-named for Linn in the 1980s. The Linn-Henley Research Library is also named in honor of Linn and his descendants. In 2005 Linn was inducted into the Birmingham Business Hall of Fame. In 2013 a statue of Linn, sculpted by Branko Medenica, was installed at Linn Park by the Alabama-Mississippi Chapter of the National Multiple Sclerosis Society. The commission honored MS campaign chair Arthur Henley.