Williams was a free agent after being released by Australian club Canberra Raiders in May.
Wigan did have an option to re-sign the player when his time in the NRL ended but reached an agreement with Williams not to enforce it, freeing him up to join the Wolves.
“I’m really excited to have signed for Warrington,” Williams told the club’s website.
“It’s a club that I’ve had plenty of tough games against in the past and the Halliwell Jones Stadium is a ground that I’ve really enjoyed playing at.
“The boys here at the club that I know from England camps spoke really highly of the organisation and the culture here. There’s some world-class talent and some real experience in this group.”
Williams, who won two Super League titles with Wigan, left the Warriors for the Raiders at the end of the 2019 season.
He made 32 appearances for the Australian side but sought an early exit, citing homesickness.
Williams said: “I’m really proud that I stepped out of my comfort zone to go out and test myself in the NRL and I like to think it’s helped me develop my game in the last 18 months, which I’m hoping to showcase now here at Warrington.
“The team has been building nicely this season and I’m just keen and excited now to come in and get started.”
He joins a team who are currently third in Super League.
Warrington chairman Stuart Middleton said: “We are delighted to have secured the services of a world-class British half-back.
“Since George’s availability became known to us he became our number one recruitment target.
“However, bringing him in midway through this year proved extremely challenging with numerous complexities attached.
“Therefore, we are immensely delighted to finally be able to announce this signing to all our loyal supporters and partners.
“I’d like to place on record my thanks to Wigan Warriors for allowing George to join us despite having a first refusal agreement.”