The abrasive midfielder has signed for Reds after spending the second half of last season with MK Dons.
The move means he is again united with Crawley boss Scott Lindsey.
Williams said: “I am delighted to be back at Crawley.
“I was driving back to the stadium today, and it just felt like home, and that I hadn’t left.
“I am buzzing to be working with Scott again, and I can’t wait to reconnect with the fans.
“Our fans are the best that I have ever played in front of, so I can’t wait to see them again.”
Williams was a popular member of the Crawley side who won promotion from League Two via the play-offs little more than year ago.
Adam Hinshelwood among fans dancing in the stand as Jack wins Euros
But he made unwanted headlines when his foul at the Amex led to a bad injury for Albion midfielder Matt O'Riley during a Carabao Cup in the opening weeks of last season.
Liverpool goalkeeper Harvey Davies, who spent last season on loan at Crewe, has joined Reds on a season-long loan.
Meanwhile Crawley striker Will Swan has joined League One new boys Bradford City as squads start to take shape for next season.