From Wiki:
Various countries around the world started to recover from the Great Depression at different times. In most countries of the world, recovery from the Great Depression began in 1933. In the U.S., recovery began in the spring of 1933. However, the U.S. did not return to 1929 GNP for over a decade and still had an unemployment rate of about 15% in 1940, albeit down from the high of 25% in 1933.
There is no consensus among economists regarding the motive force for the U.S. economic expansion that continued through most of the Roosevelt years (and the 1937 recession that interrupted it).
The common view among mainstream economists is that Roosevelt's New Deal policies either caused or accelerated the recovery, although his policies were never aggressive enough to bring the economy completely out of recession. Some economists have also called attention to the positive effects from expectations of reflation and rising nominal interest rates that Roosevelt's words and actions portended. However, opposition from the new Conservative Coalition caused a rollback of the New Deal policies in early 1937, which caused a setback in the recovery.