The three Tests take place in England on consecutive weeks at Wembley Stadium, Everton FC's Hill Dickinson Stadium and Headingley, starting on October 25.
Brimson, 27, who qualifies through his English mother, seems set to make his international debut against the Kangaroos during the three-Test series.
Announcing his squad on Monday, Wane said of the Titans man: "I needed to be convinced and I was convinced with AJ. He can play. He's a talent and can be an asset for England for many years."
Back-rower John Bateman (Cowboys), second-rower Kai Pearce-Paul (Knights), centre Herbie Farnworth (Dolphins), forward Morgan Smithies (Raiders) and winger Dom Young (Knights) complete the contingent of Australian-based players.
However, Wane made a surprise call when he claimed the Man of Steel award "doesn't mean anything" to him after omitting this year's winner, Jake Connor.
The Leeds man, who was a notable absentee from the 24-man squad, has enjoyed an outstanding season following his switch to the Rhinos but it was not enough to earn a recall.
Wane picked just three halves, with Hull KR grand final match-winner Mikey Lewis and the established pair of Harry Smith and George Williams getting the nod.
"He's a very good player, Jake, but when I'm picking a squad, what you will never hear from me is, 'He's won the Man of Steel, he needs to be in'," Wane said.
"I don't know who picks the Man of Steel, I don't know what goes into it. I don't even know who's in the Dream Team. It never comes into my reckoning, these things that mean a lot to other people.
"I just watch the players play and think who can do a fantastic job against Australia.
"It was more about his form than anything else. I don't see the obsession, why every single person (talks about) the Man of Steel. It doesn't mean anything to me."
Lewis' Rovers teammate Joe Burgess, formerly of the Sydney Roosters and South Sydney, also earned a call-up. It is winger Burgess's first involvement since 2015.
The England team will be captained by former Canberra halfback George Williams.
Veterans Alex Walmsley and Kallum Watkins, absent from the international scene since 2021 and 2022 respectively, have been recalled as England attempt to win the Ashes for the first time since 1970 against Kevin Walters' side.
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