The 17-year-old, alongside Wazny, took the title with a comfortable 6-2, 6-3 victory on court six to become the sixth Finnish junior grand slam winner.
Losing their serve in the first set had little impact as they would break Johnston and Willwerth's serve three times, while a break in the eighth game of the second set was all they needed to clinch the title.
The Finn and Pole were the second seeds for the tournament, in which they would win all five of their matches without dropping a set.
They eliminated American third seeds Keaton Hance and Jack Kennedy in the Semi-finals, while top seeds Amir Omarkhanov and Andres Santamarta Roig were beaten in the First Round.
Paldanius emulates Harri Heliovaara, who won the Australian Open boys doubles back in 2007. Heliovaara is currently a senior doubles grand slam title holder in both Australia and at Wimbledon, but at Rolland-Garros, he and partner Henry Patten were beaten in the Quarter-finals.