Simon, 33, was 15-10 with a 3.44 ERA and 127 strikeouts in 32 starts for the Reds last season.
"Alfredo Simon is a pitcher that we like a great deal and will be slotted into our starting rotation," Tigers general manager David Dombrowski said in a statement. "Alfredo had a fine season last year, made the National League All Star team, and we're excited to him have join our ballclub."
Crawford, 23, was a first-round draft pick in 2013 and went 8-3 with a 2.85 ERA this year at Class A West Michigan.
The 22-year-old Suarez hit .242 with four homers and 23 RBIs for Detroit last season.