The period in japan's history in the late 19th century when imperial rule was restored was known as the

The Meiji period.
Quates from Wiki
The Meiji period , also known as the Meiji era, is a Japanese era which extended from October 23, 1868 through July 30, 1912.[1] This period represents the first half of the Empire of Japan during which Japanese society moved from being an isolated feudal society to its modern form. Fundamental changes affected its social structure, internal politics, economy, military, and foreign relations. The period corresponded with the reign of Emperor Meiji after 1868, and lasted until his death in 1912. It was succeeded by the Taishō period upon the accession of Emperor Taishō to the throne.

Meiji Restoration - it began in 1868 under Emporer Meiji