Williams, who has 50 international caps, has agreed a three-year deal that will see him join the Ospreys ahead of next season.
The 27-year-old scored his 11th Wales try in Sunday's (AEDT) loss to New Zealand and is now relishing a new challenge, despite admitting to some sadness at leaving his old Pro14 club behind.
"I hope it goes without saying that this has not been an easy decision for me, but ultimately, I feel it is a move that is the right option for me at this time in my career," he said in a statement on the Ospreys' website.
"I've loved every minute of my 11 years at the Scarlets. I will always be grateful to the board, [head coach] Wayne [Pivac] and his team, and all associated with the club, for their support over those years
"I'm now looking forward to a fresh challenge at the Ospreys. I'm excited about the their mid- and long-term plans and goals, and my role there as a senior player. I hope it will allow me to continue improving and developing, both as a player and as a person, which is a great motivator for me.
"Once this weekend and the international period are complete, I'll be back at the Scarlets determined to positively contribute to achieving our goals for this season."
Pivac's Scarlets sit top of Conference B, while Williams' next employers are at the foot of Conference A.