Cycling Australia's (CA) support is likely to mean Cookson can rely on three votes from Oceania's regional federation, which may prove decisive in a tightly contested poll with only 42 casting voters across the globe.
CA and delegates from New Zealand and the Oceania Confederation heard manifestos from both candidates in Sydney over the weekend, and outgoing CA president Klaus Mueller said British Cycling head Cookson was the best candidate to "restore credibility" to the sport and the UCI.
"We are confident that he is genuinely committed to developing the sport worldwide and can deliver on his objectives to help grow the sport in Australia and Oceania," Mueller said in a statement on Monday.
"His commitment to introduce reforms to address the sport's governance and anti-doping challenges were critical in our considerations."
Cookson has based his candidacy on restoring trust in the UCI which was criticised heavily for not doing enough to catch drug cheat Lance Armstrong, who was stripped of his seven Tour de France titles last year.
Mueller also fired a broadside at Irishman McQuaid, who is running for a third mandate after being re-elected unopposed in 2009.
"CA has enjoyed a very good relationship with Pat over the years and we recognise the significant work he has done to help globalise the sport and address the doping culture that besieged professional men's road cycling.
"However, the inadequate response in dealing with the fallout from the Armstrong affair and subsequent allegations brought against the UCI has emphasised a need for leadership change to allow the sport to move on and realise its enormous potential."
McQuaid suffered a blow last week when he lost Switzerland's backing for his re-election bid, having already lost the support of his home federation Cycling Ireland.
The UCI constitution only allows for presidential candidates that have been nominated by their home federation. But McQuaid has pledged to fight on pending a motion to amend the constitution that would allow his nomination by any two member federations.
CA said it would not support the motion.
"Even if those changes are legal it is entirely unsatisfactory in any democratic process and it lacks openness, transparency and integrity," Mueller said.
The election will be held at the UCI general congress in Florence on September 27, during the road world championships in Tuscany.
(Reporting by Ian Ransom; Editing by Greg Stutchbury)
