Bradley, who was most recently in charge of Norwegian side Stabaek, has signed a two-year deal in Normandy.
The 57-year-old took the USA to the last 16 of the World Cup in South Africa in 2010 and has also been the coach of Egypt.
"To come and coach Le Havre is a new challenge in my career. I will lend all my experience and expertise to help the club get back into the elite and lay the foundations of an ambitious and solid project," Bradley said in a statement on the club's website.
The oldest professional club in France, Le Havre, whose president is an American, are currently fourth in Ligue 2.