Thomas, 21, has agreed a three-year deal at Rugby Park after requesting a move from Fir Park.
He moved to Motherwell from Celtic's youth set-up in 2014 and spent the second half of last season on loan at Queen of the South.
He scored three goals in 17 appearances for the Doonhamers.
Thomas, who had a year to run on his contract, started just four games for Motherwell, with a further 33 appearances from the substitutes' bench.
"I wanted to have a look at Dom over the first few weeks of pre-season, but he expressed a desire to move on from the club," manager Stephen Robinson told the 'Well website.
"This deal allows the lad to try and advance his career but also protects Motherwell FC's interests in the longer term, so it suits all parties."
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The 21-year-old, who has been playing for Icelandic side IBV this summer, has signed a one-year deal.
"I'm looking forward to a new chapter in my career.
"It was disappointing that I didn't play more Premier League football, but sometimes you have to take a step back to go forward again," the right-back told the League One club's website.
"I know a couple of the other lads and I've had a good spell in Iceland so I feel fit and raring to go."
James is a terrific defender but he loves to get forward and fits the template of player I want in our squad
Hurst, who has represented England at Under-16, Under-17, Under-19 and Under-20 level, spent time on loan at Birmingham and Shrewsbury last season.
He began his career at Portsmouth, but failed to make a senior appearance at Fratton Park and moved to West Brom in 2010 following a previous loan spell with IBV.
He was restricted to three appearances in all competitions for the Baggies and had five separate loan spells away from the Hawthorns during his time with the Premier League side.
Crawley manager Richie Barker said he was delighted to secure Hurst's signature.
"Right-back was a key position for us when it came to adding to the squad," Barker said.
"He's a terrific defender but he loves to get forward and fits the template of player I want in our squad - someone who is young, athletic with a willingness to learn and improve and [has] a terrific attitude."

Chelsey Lee, 26, played for Bucheon KEB Hana Bank in the Women's Korean Basketball League (WKBL), whose teams are allowed only two foreign players.
Prosecutors were asked to investigate after the Korean Olympic Committee pushed for Lee's naturalisation.
The WKBL says Lee will be suspended for life and her records annulled.
The Miami-born centre won the league's rookie of the year award in the 2015-16 season after helping her team reach the championship series.
However, Lee and her two agents are suspected of fabricating her and her father's birth certificates to show she had a South Korean grandmother.
Bucheon KEB Hana Bank issued a public apology, vowing to take legal action against Lee and her agents.
The club's owner and head coach will step down.
WKBL commissioner Shin Sun-woo said the team's records and ranking will be nullified and the league will scrap the extra quota for international players with a Korean parent or grandparent.
Kilmarnock have signed Dom Thomas, following the attacking midfielder's release from Scottish Premiership rivals Motherwell.
[NEXT_CONCEPT]
Crawley Town have completed the signing of former West Brom defender James Hurst on a free transfer.
[NEXT_CONCEPT]
An American basketball player has been banned from South Korea's domestic league for life after prosecutors said she forged her birth documents.