Leeds's return to the top flight after a 16-year wait was clinched as Huddersfield Town beat West Bromwich Albion 2-1 in the Championship on Saturday (AEST).
Manchester City boss Guardiola has previously labelled Bielsa as the best coach in the world.
A post on his PepTeam Twitter account read, in Spanish: "The best reaches the @premierleague."
Liverpool's James Milner, who made his debut for hometown club Leeds at 16, wrote: "Congratulations LUFC, #backwhereyoubelong."
City defender Benjamin Mendy played under Bielsa at Marseille and wrote: "Congratulations Marcelo & the boys see you next year."
LEEDS 💙💛 congratulations Marcelo & the boys 🔥 see you next year— Benjamin Mendy (@benmendy23) July 17, 2020