Bajin became the first recipient of the WTA Coach of the Year award in 2018 after helping Osaka to her maiden WTA title at Indian Wells and US Open glory in September.
Osaka made it successive grand slam crowns with victory at the Australian Open at the start of 2019, sending her to the top of the world rankings.
However, just over two weeks after triumphing at Melbourne Park, Osaka announced her surprise split from Bajin.
Mladenovic, 66th in the WTA rankings, confirmed she would be working with the German.
"I am very excited to announce [to] you my new collaboration with Sascha Bajin. Welcome to the team, coach," the Frenchwoman posted on Twitter.
Mladenovic has a 5-7 record in main-draw Tour-level matches this year, including a first-round exit at the Australian Open and a second-round loss to Osaka at Indian Wells.