Britain's largest bookmaker had announced the purchase last year of three American companies but the deal was conditional on the granting of the licence.
The green light from the Nevada Gaming Commission allows the British firm to begin offering sports betting on mobile devices. Online gambling is currently illegal in the US but William Hill will be well-positioned to move fast if the restriction is lifted.
"This now enables us to establish William Hill's first ever U.S. operation, an important part of our international growth strategy," said chief executive Ralph Topping.
The company would combine its own brand and product range with the local footprint established by the three firms - AWI, Brandywine and Cal Neva, he said.
The acquisitions are expected to be completed on June 27 for approximately $49m in total.