Double Fine Productions announced that both adventure titles will be available for the Android console, but did not indicate whether this will be at launch.
"Reds is coming to Ouya, the upcoming Android-based console that had its own big Kickstarter last year. Lots of our fans have requested this, but we weren't able to commit to it until now," said Double Fine in a statement.
"We've worked out a deal with the makers of Ouya that will actually result in some extra money for the Reds budget, so it worked out well all around.
"We're also planning on bringing The Cave, our most recent release, to the system. We'll have more details about this down the road."
Reds - also known as Double Fine Adventure - is a crowd-sourced point-and-click title from Grim Fandango creator Tim Schafer due for release later this year.
The Cave is a title with similar gameplay developed by The Secret of Monkey Island programmer Ron Gilbert, released for PC, Wii U, Xbox 360 and PlayStation 3.
Ouya will launch this June in North America and will retail for $100 (£63).
Watch a trailer for The Cave below: