The Wanderers received permission from Newcastle to approach Robinson, the Jets' head coach, on Wednesday just two days after the Sydney club sacked Jean-Paul de Marigny.
On Thursday, Robinson officially departed the Jets and joined the Wanderers, with assistant Kenny Miller also moving from Newcastle to Western Sydney.
"Sometimes in football you get an opportunity too good to turn down," Robinson said. "This is a fantastic football club, a big club in the A-League and one that has set the foundations to be very successful.
"There is an expectation of winning that is clear and that is what I am here to do -- have success on the pitch and create a pathway for our future players at the club."
Former Wales international Robinson replaced Ernie Merrick at Newcastle on a three-and-a-half-year deal in February.
He quickly turned Newcastle's form around, leading the Jets to six wins, three draws and one loss from 10 games, falling just short of the top six.
Robinson, 44, coached MLS side Vancouver Whitecaps from 2013 to 2018 and will become Western Sydney's fourth full-time coach in as many seasons as they look to recapture the spark of the club's early days under Tony Popovic.
"Carl has a great track record both here and in the MLS, his knowledge and passion for the game is inspiring and he comes with a great attitude that will be well-received by our amazing members and fans," Wanderers chief executive John Tsatsimas said.
"Once we realised Carl was a potential option we moved quickly to bring him in as we have had only highly positive reports on him as a coach and as a leader of men."
Inaugural coach Popovic resigned days before the start of the 2017-18 A-League season and the Wanderers haven't made the finals in the three seasons since his departure.