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The pair beat the reigning Wimbledon champions 6-2, 6-1 in 1hr 12mins to claim their third Grand Slam title together and 10th overall.
Mladenovic, who won the Fed Cup with France in Perth in November, also reached last year’s Melbourne doubles final with Babos, going down to Sam Stosur and Zhang Shuai.
“There’s just something about Australia we love coming back. Our performance becomes better and better each time,” said Babos.
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Hsieh and Strycova warmed up for the Australian Open by winning in Brisbane and did not drop a set in their run to the final.