The Athletic Bilbao forward is one of 10 uncapped players in the squad for those games, having scored 13 games in all competitions this season.
His inclusion in the national squad at the age of 21 represents a rapid rise for Williams, who has lofty ambitions.
"I did not expect to be here. Everything was very fast. I am very grateful and very excited," Williams said.
"I'm meeting my deadlines. I want to strengthen my place in the team and in the selection and hope to be one of the leaders in the selection in future."
Asked if he could force his way into the squad for Euro 2016, Williams replied: "Until the last day everything is possible."