Alexander, 30, shares the record-setting mark of 72 caps for an Australia Test prop with Waratahs loosehead and international team-mate Benn Robinson.
Sydney-born Alexander first signed with the Brumbies in 2008, the same year he made his international debut for Australia against France.
He played in the 2011 World Cup and started all three matches against the British and Irish Lions in 2013 as well as touring Europe with the Wallabies at the end of last year.
In April, the Australia Rugby Union relaxed its eligibility criteria to allow senior players – those with at least 60 Australia caps – at overseas clubs to represent the Wallabies after facing a mass exodus of top names following this year’s World Cup.
Before this, players based abroad were unable to represent their country.
“I am extremely grateful for the opportunities rugby has given me in this country and when I weighed everything up in deciding my future, it became quite clear that this is where I want to be,” Alexander said.
“Representing the Wallabies and the Brumbies is something I’m very passionate about, and I feel both teams are trending in the right direction to have plenty of success over the next few years.”
The front-row said he hoped to use the experience of the 2011 world tournament, which ended in a 20-6 defeat to hosts and eventual champions New Zealand, to his international team’s advantage this year.
“While the end result wasn’t what we wanted, it was a great experience being part of the World Cup in 2011 and it is something I would love to be part of again,” he said.
“The squad learned a lot from the tournament and I’m sure those players who took part will be a lot better for the experience this time round.
“There is no doubt that World Cups are really special events, so I’m just working as hard as possible to put my hand up for selection when the moment arrives.”