When Does “The Last Samurai” (2003) Take Place?
"The Last Samurai" is a historical fiction film written by John Logan with Edward Zwick and Marshall Herskovitz that released December 5th, 2003. So when is "The Last Samurai" set?
It takes place in the years:
We know this because the film's main action loosely depicts a combination of the early part of the famous and tragic Boshin War (a.k.a. the Japanese Civil War), which lasted from 1868 AD to 1869 AD, but more of the latter part of the famous and tragic but even more short-lived Satsuma Rebellion, which occurred from just January 29th, 1877 AD to September 24th, 1877 AD. Captain Nathan Algren’s narration, at the start of the main action, takes the form of a journal dated "July 12th, 1876" and, very soon after, there is a time and place setting title card over the footage: “Yokohama Harbor, 1876”. So the story seems to start in July of 1876 AD.

1876 AD - 1877 AD
We know this because the film's main action loosely depicts a combination of the early part of the famous and tragic Boshin War (a.k.a. the Japanese Civil War), which lasted from 1868 AD to 1869 AD, but more of the latter part of the famous and tragic but even more short-lived Satsuma Rebellion, which occurred from just January 29th, 1877 AD to September 24th, 1877 AD. Captain Nathan Algren’s narration, at the start of the main action, takes the form of a journal dated "July 12th, 1876" and, very soon after, there is a time and place setting title card over the footage: “Yokohama Harbor, 1876”. So the story seems to start in July of 1876 AD.
Algren spends the late Fall and, as his journal entry dates tells us, through “Winter, 1877.” and into “Spring, 1877.” in a fictionalized version of the Satsuma province.
These dates are historically possible but historically complicated because Algren is loosely based on the real-world French naval military leader Eugène Collache (1847-1883), who was in Japan only during the duration of the Boshin War, a decade previous to the dates the character writes in his journal. In the real-world, the primary Western countries helping to modernize Japan's military were European not the United States of America and the Boshin War battles most similar to those in the movie were fought between ships and not on land. Moritsugu Katsumoto (one of "The Last Samurai" of the film's title) is based on the real-world Saigō Takamori (1828 -1877), a samurai who led the anti-Imperial, anti-modernization forces in both the Boshin War and the Satsuma Rebellion, which did end in a land battle. The fictionalized version of this battle is on or just after "May 25th, 1877.", as dated by Algren’s journal (while the real-world equivalent happened on September 24th). So the story ends in May or September of 1877 AD.
Additionally, the movie’s prologue has another time and place setting title card reading "San Francisco, 1876" so it’s within the same years as the main part of the narrative. HOWEVER, the story’s first half includes multiple flashbacks to Algren’s time in the American Army during the post-Civil War "American Indian Wars" and before the beginning of the story. These are unplaceable but must occur sometime between May of 1865 AD (when the American Civil War ended) and July of 1876 AD (when the film begins).