More than 28,000 advance tickets were sold for Turner Whistler Monet, which examines the influence of J M W Turner on the two younger men, who were friends and rivals.
"Their work and aims made a vital contribution both to the development of Impressionism, the art movement that emerged in the 1870s, and the evolution of a symbolist landscape," a Tate spokesman said.
The ticket sales total was more than double the previous Tate record - 13,500 for Edward Hopper at Tate Modern.
The show's recent run in Paris attracted more than half a million visitors.
This exhibition runs until 15 May. Entry is pounds 10. Organisers are considering opening for 24 hours towards the end of the run if demand supports it.Reuse content