Soft contact lenses were a big invention in the field of contact lenses. It dates back to 1959-60 when Otto Wichterle and Drahoslav Lim first developed soft lenses. These were much better than earlier versions of lenses which were very hard for the eyes. Being first lenses to allow oxygen permeability to the eyes, they soon become quite popular.
However, you would be surprised to know that a lot of names are linked with the invention of first contact lenses. There is no single name you can attribute the invention of contact lens. From 1500 to 2000 a lot of research and development has taken place in the field and several names are associated with the development of contact lenses. Some of the prominent names are:
Leonardo da Vinci(For conceptualostaion in 1508)
Thomas Young (1801)
Sir John Herschel(1845)
Adolf Eugen Fick (1887)
Louis J. Girard (1887)
William Feinbloom (1936, introduced plastic lenses)
Otto Wichterle and Drahoslav Lim (developed soft lenses in 1960s which got approved in 1970 by FDA).