Final answer:
Henri Toulouse-Lautrec is the artist known for his posters of the Moulin Rouge. His work captured the essence of Parisian nightlife and was characterized by a limited color palette and distinctive composition, which made him famous.
Step-by-step explanation:
The nineteenth-century French artist renowned for his innovative layout design in posters for the Parisian nightclub, the Moulin Rouge, is Henri Toulouse-Lautrec. Toulouse-Lautrec was well-known for capturing the lively and often risqué atmosphere of the cabarets of Paris, particularly through his advertising artwork. His posters, such as 'Moulin Rouge: La Goulue', became iconic, exemplifying the vibrancy of Parisian nightlife through the use of limited colors and bold composition. These works also reflected the influence of Japanese woodblock prints and the shift towards modern advertising techniques.
Henri Toulouse-Lautrec was born into an aristocratic family, and despite his physical challenges due to an undiagnosed condition affecting his legs, he became a prolific artist. He lived most of his life in Montmartre, the bustling arts district of Paris, where he was exposed to the bohemian lifestyle and found inspiration for his artwork. There, he created posters for the Moulin Rouge that were so popular that they were frequently stolen from where they were displayed on the Paris walls.