Tycoon began as a diplomatic workaround. It was a title invented so that Japan's real ruler would not have to call himself king.
In the Edo period, power sat with the Tokugawa shogun, while the emperor remained the formal head of state. That created a problem in letters to foreign governments. The shogun could not call himself emperor, and Wikipedia notes that the word for king was also judged unsuitable. The shogunate's answer was Nihon-koku Taikun, "Tycoon of Japan." Etymonline says the shogun's supporters used it with foreigners to stress his importance over the emperor.
Taikun is written 大君. Both characters come from Chinese, one meaning "great" and the other "lord" or "ruler." So the word is Chinese in its parts and Japanese in its use.
Americans ran into it once Japan opened to them. Townsend Harris, the first American consul general in Japan, wrote it in his diary on 28 October 1857 and glossed it as "Great Ruler." Etymonline dates the English word to that same year.
It spread in 1860, when a Japanese diplomatic mission visited the United States. According to the lexicographer behind Word Histories, the White House reception drew heavy newspaper coverage, and the title came with it. On 28 May 1860 the New Orleans Daily Crescent called Senator William Henry Seward the "Tycoon" of the Black Republicans. That is the earliest known use of the word for a powerful person rather than the shogun.
The best-known early example belongs to Abraham Lincoln. His secretaries John Hay and John Nicolay called him "the Tycoon" among themselves. Etymonline cites Hay's diary from 1861, and Word Histories quotes an entry of 25 April that year. The Oxford English Dictionary has treated Lincoln as the start of the wider sense. Word Histories argues that the Seward citation shows the usage was already in the air a year earlier.
The business meaning, a rich and powerful industrialist, came last. Etymonline dates it to after World War I. By then the shogunate had fallen, and the title had outlived the office it was made for.