Williams said it was “an exciting time to be joining Newcastle” as they enter a period of new ownership, reflected in their team name.
“I came up to speak to [director of rugby] Steve Diamond, to see the set-up and hear his plans for how it is all going to evolve, and I’m just keen to get into it,” Williams said.
Williams is the 14th player signed by Newcastle since energy drinks company Red Bull became involved with the club.
They begin their league campaign on Friday with a home match against Saracens.
Williams has featured in five Tests for the British and Irish Lions and made 93 appearances for his country, and he remains hopeful of reaching his century of Test caps.
“I’ve not called time on that, but it would be impossible without a club,” he told the BBC this month.
“If I start playing regularly and there are some injuries in the back three, then Steve [Tandy, Wales head coach] may give me a call.”