The basic device was invented in 1940 by the Canadian Norman Breakey (born 1891- died aft. 1940). Breakey was never able to produce his invention in large enough numbers to profit from it before others made small changes to the paint roller's design and were able to market it as their own invention.
One of the others was Richard Croxton Adams who held the first U.S. patent on the paint roller. He claimed to have developed it in his basement workshop in 1940 while working for the Sherwin-Williams Paint Company.