The Hungarian-French pairing battled past second seeded Russians Ekaterina Makarova and Elena Vesnina 6-4, 6-3 on Rod Laver Arena.
"It's an incredible feeling, I was in tears," said an emotional Babos. "It's amazing to play with you," she added of Mladenovic.
It was their first Slam title after going close at Wimbledon in 2014, where they made the final but lost.
Overall, they own three other doubles titles as a team, all won in 2015 -- at Dubai, Marrakech and Rome.