Bielsa oversaw attractive pass and move football at Leeds as they finished the Championship with 83 points, their highest tally since they were promoted from League One in 2009-2010.
However, in this season's promotion play-offs Leeds let a 1-0 first-leg semi-final lead slip at home against Derby County and lost 4-3 on aggregate over the two legs to end their hopes of a return to the Premier League.
"Leeds United are delighted to confirm that chairman Andrea Radrizzani has officially exercised the option to extend Marcelo Bielsa's contract for a second season," Leeds said on Tuesday.
Bielsa had an eventful first season with the Whites after a club employee, acting his instruction, was discovered outside Derby's training ground ahead of a match between the sides.
Chairman Radrizzani said Leeds will be seeking a return to the top-flight for the first time since 2004.
"We were close and next season we will work harder to achieve our goal. So, let's have another go. I am delighted that Marcelo has agreed to stay for another year - we have unfinished business," Radrizzani said.