The Orioles also gave Elias the title of executive vice president.
Elias has overseen amateur scouting for the Astros since 2012. He received the assistant GM title in 2016, when he also took the lead on Houston's player development and minor league operations.
The Orioles are replacing Dan Duquette, who was fired along with manager Buck Showalter in October after a 47-115 season.
One of Elias' first tasks will be hiring Baltimore's next manager. Showalter had been the skipper since 2010.
Elias will be introduced in a news conference Monday.