The 20-year-old has moved to the Championship side on a temporary basis after a deal was completed on transfer deadline day.
Williams, a Premier League and FIFA Club World Cup winner, has made 33 appearances for Liverpool's first team, having joined the club's Academy set-up at U9 level.
The Wales international will now head to Craven Cottage for the rest of the current campaign, with Marco Silva's side currently five points clear at the top of the Championship.