The museum opened on October 4, 1992, the centenary of the birth of poetess Marina Tsvetaeva. Preparation for its establishment began back in 1988.

The museum is located in the restored "House of Tyo." This wooden one-story building in the center of Tarusa was purchased in 1899 by Marina Tsvetaeva's maternal grandfather, A.D. Mein. After his death, the house was inhabited by the grandfather's second wife, whom the young sisters M. and A. Tsvetaeva called "Tyo." The Tsvetaev family often visited here not only in the summer but throughout the year. Marina Tsvetaeva came here in the summer of 1912 with her husband Sergey Efron. In 1903, Tyo specially built a neighboring guest wing for the Tsvetaevs. This preserved one-story wooden wing was bought from the owners and transferred to the museum thanks to the support of the governor of the Kaluga region, A.D. Artamonov.

The museum's exhibition is dedicated not only to the Tsvetaev family but also to their Tarusa relatives, the Dobrotvors, as well as family friends. The themes of the halls speak for themselves: "The Arrival of the Tsvetaevs in Tarusa," "The Life and Work of M. Tsvetaeva," "The Tsvetaev Family," "The Tsvetaevs' Circle in Tarusa," "Grandfather's Study." The museum plans to create a Tsvetaev estate, including both buildings.

The foundation of the museum's collections consists of memorial items: furniture, dishes, and other belongings of the Tsvetaev family, their relatives, and friends; personal items, documents, and original photographs; books with autographs of Marina Tsvetaeva, her lifetime editions, letters, autographs of family members and well-known cultural figures, drawings and watercolors by Tsvetaeva's daughter Ariadne Efron, a large collection of antique books in Russian and foreign languages, and much more.

The museum annually hosts Tsvetaev celebrations, children's festival-competitions, scientific readings, literary-musical salons, and other cultural events.