Latos, 29, went 6-2 with a 4.62 ERA in 11 starts for the Chicago White Sox last year, was released, then was 1-1 with a 6.52 ERA in one start and five relief appearances for Washington.
"I'm happy to just be playing baseball, let's be honest," Latos said after his deal was announced Thursday.
An eight-year major league veteran, Latos is 71-58 with a 3.60 ERA. He also has pitched for San Diego (2009-11), Cincinnati (2012-14), Miami (2015), the Los Angeles Dodgers (2015) and the Los Angeles Angels (2015).
He had arthroscopic left knee surgery in 2014 to remove his medial meniscus and had swelling during the following two seasons that affected his range of motion and strength.
Latos' big league role for now might be in the bullpen, or he could go to Triple-A Buffalo and start there in case an opening occurs in Toronto.
"Whatever it comes down to is what it comes down to," he said. "I just want to get back to me and how I used to pitch."