Voges will coach WA for the final time in the upcoming Sheffield Shield clash with NSW, starting on March 14.
Casson has served as Voges' assistant for the past seven years at both WA and the Perth Scorchers.
Before that, Casson spent five seasons in Sydney as an assistant coach for both NSW and Sydney Thunder.
Casson, a left-arm wrist spinner, played one Test for Australia in 2008 along with 53 first-class matches before retiring at the age of 28 due to a heart condition known as Fallot's syndrome.
The 43-year-old, who was taken to hospital mid-game in 2011, has undergone multiple heart surgeries to address the issue.
Casson has big shoes to fill after Voges guided WA through a golden era that yielded a hat-trick of Shield titles as well as four one-day crowns.
Voges, who also steered the Perth Scorchers to three T20 titles, will stay on in that BBL role, leaving Casson purely in charge of WA.
Casson's three-year deal starts from next season.
"I've thoroughly enjoyed the opportunity to work with Adam Voges and the remainder of the coaching staff over the past seven seasons and have been proud of what we have been able to achieve in that time," he said in a statement.
"Adam did a wonderful job to create an environment that brought the best out of all our players, which is something I'm looking forward to building on.
"I want our players to strive for excellence and give them the best opportunity to push for higher honours.
"I am confident we have the playing group that can bring WA more success in both formats of the game."
Along with staying on with the Perth Scorchers, Voges has been announced as head coach of the Seattle Orcas in Major League Cricket.
The 46-year-old is being heavily tipped to become Australia's next coach given the level of success he achieved with WA.
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