Here is the list of the most visited museums in the world for the year 2019. A museum is defined as a building or institution dedicated to the acquisition, care, research, and exhibition of numerous objects that represent the legacy of humankind and its environment.
For this top 10, 4 museums are from United Kingdom, 2 from the United States, and one each from China, Russia, France, and Vatican City.

Table of Contents:
👉 State Hermitage Museum
👉 American Museum of Natural History
👉 Natural History Museum
👉 National Gallery
👉 Tate Modern
👉 British Museum
👉 Metropolitan Museum of Art
👉 Vatican Museums
👉 National Museum of China
👉 Louvre

Top 10 Most Visited Museums in the World

👉 Number 10 - State Hermitage Museum
The State Hermitage Museum is a museum of art and culture in Saint Petersburg, Russia. The second-largest art museum in the world, it was founded in 1764 when Empress Catherine the Great acquired an impressive collection of paintings from the Berlin merchant Johann Ernst Gotzkowsky. The museum has 4,956,529 visitors per year as of 2019.
👉 Number 9 - American Museum of Natural History
The American Museum of Natural History is a natural history museum on the Upper West Side of Manhattan, New York City. The museum has 5 million visitors per year.
👉 Number 8 - Natural History Museum
The Natural History Museum in London is a natural history museum that exhibits a vast range of specimens from various segments of natural history. It is one of three major museums on Exhibition Road in South Kensington, the others being the Science Museum and the Victoria and Albert Museum. It has a total of 5,424,000 visits per year.
DAVID ILIFF

👉 Number 7 - National Gallery
The National Gallery is an art museum in Trafalgar Square in the City of Westminster, in Central London. Founded in 1824, it houses a collection of over 2,300 paintings dating from the mid-13th century to 1900. The Gallery is an exempt charity, and a non-departmental public body of the Department for Digital, Culture, Media and Sport. It has a total visits of 6,011,007 per year.
The National Gallery, Trafalgar Square. Image courtesy of the National Gallery.

👉 Number 6 - Tate Modern
Tate is an institution that houses, in a network of four art galleries, the United Kingdom's national collection of British art, and international modern and contemporary art. It is not a government institution, but its main sponsor is the UK Department for Digital, Culture, Media and Sport. It has a total visits of 6,098,340 per year.
Herzog and De Meuron: Tate Modern

👉 Number 5 - British Museum
The British Museum, in the Bloomsbury area of London, England, is a public institution dedicated to human history, art and culture. Its permanent collection of some eight million works is among the largest and most comprehensive in existence, having been widely collected during the era of the British Empire. It has a total visits of 6,239,983 per year.
The British Museum © Courtesy the Trustees of the British Museum

👉 Number 4 - Metropolitan Museum of Art
The Metropolitan Museum of Art of New York City, colloquially "the Met", is the largest art museum in the United States. Its permanent collection contains over two million works, divided among 17 curatorial departments. It has a total visits of 6,479,548 per year.
metmuseum.org

👉 Number 3 - Vatican Museums
The Vatican Museums are the public art and sculpture museums in the Vatican City. They display works from the immense collection amassed by the Catholic Church and the papacy throughout the centuries including several of the most renowned Roman sculptures and most important masterpieces of Renaissance art in the world. The museums contain roughly 70,000 works, of which 20,000 are on display, and currently employ 640 people who work in 40 different administrative, scholarly, and restoration departments. It has a total visits of 6,882,931 yearly.
Calin Stan / shutterstock.com

👉 Number 2 - National Museum of China
The National Museum of China is 2nd on the list with  7,390,000 visit per annum. The National Museum of China flanks the eastern side of Tiananmen Square in Beijing, China. The museum's mission is to educate about the arts and history of China. It is directed by the Ministry of Culture of the People's Republic of China.
👉 Number 1 - Louvre
The number on the list is the Louvre Museum with 9,600,000 visits yearly. The Louvre, or the Louvre Museum, is the world's largest art museum and a historic monument in Paris, France, and is best known for being the home of the Mona Lisa. A central landmark of the city, it is located on the Right Bank of the Seine in the city's 1st arrondissement.
References:
👉 State Hermitage Museum, Wikipedia.org
👉 American Museum of Natural History, Wikipedia.org
👉 Natural History Museum, Wikipedia.org
👉 National Gallery, Wikipedia.org
👉 Tate Modern, Wikipedia.org
👉 British Museum, Wikipedia.org
👉 Metropolitan Museum of Art, Wikipedia.org
👉 Vatican Museums, Wikipedia.org
👉 National Museum of China, Wikipedia.org
👉 Louvre, Wikipedia.org
👉 List of most-visited museums, Wikipedia.org