The English heavyweights announced on Friday they had signed the Australian on a two-year deal, with head coach Jonas Eidevall calling her "one of the best young players in world football".
Cooney-Cross, an A-League Women title-winner with Melbourne Victory, was super delighted to move from Swedish club Hammarby.
"I'm so excited to join this club. Arsenal just felt right as soon as I heard about the interest," she said.
The move took place late on Thursday on the final day of the transfer window.
Arsenal have reportedly paid $A270,000 to sign the 21-year-old, a hefty sum in the women's game.
Cooney-Cross joins fellow Matildas stars Steph Catley and Caitlin Foord at the Gunners, who finished third in the Women's Super League last season.
The Queensland-born talent was one of Australia's best during their World Cup run during which she proved to be a powerful force in the middle of the park, belying her age.
Despite being the second-youngest member of Tony Gustavsson's squad, she played all but four minutes of the Matildas' seven matches - an endorsement of her importance.
Eidevall said he was delighted to secure her services for the forthcoming campaign.
"Her passing ability and explosiveness allow her to affect games in a way you rarely see from such a young player, so we firmly believe she will be an excellent addition to our midfield, now and in the future," he said.
Cooney-Cross is a product of the A-League, debuting as a 15-year-old for Victory in 2017 and also playing for Western Sydney before her shift to Europe.
She joins a strong Australian contingent in the English top flight, including superstar forward Sam Kerr (Chelsea), fellow young gun Mary Fowler (Manchester City) and goalkeeper Mackenzie Arnold (West Ham).
The Women's Super League season begins in a fortnight.
22°C