It includes continuing with the series and developing spin-off Prison Break: Cherry Hill.
Chairman Gary Newman commented: "Prison Break is an amazing series for the studio, impacting audiences around the world, and much of that is due to the excellent showrunning Matt has done on it.
"We're looking forward to him continuing his leadership on Prison Break and also creating his own shows."
Fox has commissioned scripts for Cherry Hill, set in a women's prison, which Olmstead is writing with co-executive producer Zack Estrin.
He has been at the studio for nearly ten years and thanked its chairmen Newman and Dana Walden: "I wanted to stay, because it's been great here. Dana and Gary are protective and encouraging, and they have a very collegial relationship with the Fox network."
Olmstead added that Prison Break was in a strong position to carry on if and when he focuses on the spin-off: "Its staff is completely populated by first-draft writers and future showrunners.
"If we have to go work on the spin-off, there are plenty of heavy hitters at Break to help out."