Favre will replace Peter Stoeger, who had been in charge BVB since December last year, but whose contract was not extended due to disappointing results.
Borussia finished the season in fourth place, 29 points behind leader Bayern Munich, and the losing finalists in 2013 under then-manager Jurgen Klopp only just squeezed into a spot for next season's Champions League.
Favre is a seasoned hand in the Bundesliga, having led Hertha to fourth place in the 2008-2009 season.
In 2011-2012, he took the driving seat at Borussia Moenchengladbach when the club was languishing at the bottom of the table. He saved them from relegation and then built them up into a solid mid-table side.
"Training Borussia Dortmund is an appealing task that I am taking on gladly... We will now build a new team together," said Favre.
Favre led Nice to a third-placed finish last season, although they lost in the Champions League playoff round to Napoli last August.
But this term a poor start to their league campaign proved costly, as Saturday's 3-2 loss at Lyon ensured they finished eighth and missed out on European football next season altogether.
Favre's new contract at Dortmund runs to June 30, 2020.