The first Fender amps were produced between 1945 and 1946 by the K&F Manufacturing Corporation, which was run by Leo Fender and Doc Kauffman. Leo Fender began building guitar amps before he started manufacturing guitars. The original Fender amps were tube-powered and the company also started producing solid-state models in the late 1960s.
For a detailed history refer to Fender Amps: The First Fifty Years from author John Teagle.