Athletic defeated Mallorca in a penalty shootout on Saturday.
Williams said: "I have many years left here, I am calm and happy. Looking forward to getting to Bilbao to celebrate.
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"From the park to here. My family deserves it, my parents have worked hard. This goes to all those people who are with me every day, I hope you enjoy it a lot.
"I have dreamed of this moment many times. Last year I had two chances that I didn't score and we were on the verge of reaching the final. I am very happy to make history and have a name in the club.
"I was the first one to cry, I don't even want to imagine it. The fans deserve everything and more, they have always been with us."