Reading from the official rules it will be Bo3 Conquest with one ban. It will be a Swiss Tournament with Single Elimination playoffs, much like the regional Championships are. If there are a lot of players, there will be multiple brackets and the brackets are played in two separate days should there be more than 129 players in the tournament.
For more info, here's a direct link to the rules. Chapter 4.5 on 8th page for Challenger Finals rules.
(And thanks for that link AUzg, couldn't find the link to the rules from Blizzard's official site even though I knew I had seen the rules before. Blizz please. And good luck with your challenger cups too!)