Williams, who has been with the club since 2013, has put pen to paper on a contract extension that also sees his release clause rise by more than 50% compared to the one in his original contract, meaning it will near 80 million euros.
Speaking about his new deal, Williams said: "When it comes to making decisions, for me, the most important thing is to listen to your heart. I am where I want to be, with my people, this is my home."
Given registration issues, any move to Barcelona will not happen this summer, according to Fabrizio Romano.
Williams, who plays alongside brother Inaki at San Mames, made his debut for the club back in 2021. Since then, he has flourished, making 131 LaLiga appearances, scoring 16 goals in that time, as well as 15 in other competitions.
He has also represented Spain at international level, playing a major part in his country's run to the European Championship title in 2024.
Athletic Club finished fourth in LaLiga last season, qualifying for the Champions League in the process. They also made the Europa League semi-finals last year, eventually bowing out to Manchester United.
Barcelona, meanwhile, have spent the summer chasing Williams, and now will need to look elsewhere for a pacey winger. According to reports, talks with Liverpool's Luis Diaz have broken down, meaning they will need to head back to the drawing board to find their next target.