Free agent Williams, 28, left Reading at the end of last season after four years with the Championship side. He played 45 matches last campaign as the Royals finished third but lost the play-off final to Huddersfield.
Palmer, 20, scored five goals in 27 appearances for Huddersfield last campaign and re-joined the club on loan for the 2017-18 season after signing a four-year deal with Chelsea.
Eight players have signed for manager David Wagner's side as they prepare for their first season in the top tier for 45 years.
(Reporting by Aditi Prakash in Bengaluru; Editing by Hugh Lawson)
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