Toomua ruled out of Bulls showdown
Moore and Alexander missed last week's 10-23 loss to the Highlanders in Invercargill, but will rejoin the starting side - along with Scott Sio, who came off the bench last week.
Sio replaces Allan Alaalatoa who returns to the replacement bench.
Lock Rory Arnold, who also started last week's match from the bench, returns to the starting XV alongside Sam Carter, while the back row trio of Scott Fardy, David Pocock and Jarrad Butler remains unchanged.
Tomás Cubelli and Christian Lealiifano remain the halgback pairing, while the versatile Robbie Coleman gets his first start at inside centre - with Toomua ruled out with a knee injury.
Toomua left the field in the 73rd minute of the Brumbies' loss to the Highlanders last week and has not recovered in time for this week's match.
Tevita Kuridrani will start at outside centre, while Nigel Ah Wong and James Dargaville are the new starting wings.
It will be Dargaville's first start in 2016 after featuring in four matches this season from the bench.
Aidan Toua will start the match at fullback.
Last week's starting front row of Alaalatoa, Josh Mann-Rea and Ruan Smith will all start from the bench, along with Tom Staniforth, Blake Enever, Jordan Smiler, Joe Powell and Lausii Taliauli.
The Brumbies have won three of their last four matches against the Bulls including last year's 22-16 win in Canberra.
A brace of matches against New Zealand opposition leaves the Brumbies with a streak of two losses going into this fixture.
The last time they lost more than two matches in a row in Super Rugby was in Round 13, 2011.
Brumbies: 15 Aidan Toua, 14 Nigel Ah Wong, 13 Tevita Kuridrani, 12 Robbie Coleman, 11 James Dargaville, 10 Christian Lealiifano (co-captain), 9 Tomás Cubelli, 8 Jarrad Butler, 7 David Pocock, 6 Scott Fardy, 5 Sam Carter, 4 Rory Arnold, 3 Ben Alexander, 2 Stephen Moore (co-captain), 1 Scott Sio.
Replacements: 16 Josh Mann-Rea, 17 Allan Alaalatoa, 18 Ruan Smith, 19 Tom Staniforth, 20 Blake Enever, 21 Jordan Smiler, 22 Joe Powell, 23 Lausii Taliauli.
Date: Friday, May 7
Venue: GIO Stadium, Canberra
Kick-off: 19.45 (11.45 SA Time, 09.45 GMT)
Referee: Ben O'Keeffe
Assistant referees: Will Houston, Ed Martin
TMO: Peter Marshall