The 28-year-old Willis was designated for assignment on Sunday, giving the Tigers up to 10 days to make a move with him. He was making $12 million this year.
Willis was 1-2 with a 4.98 ERA this season. The former NL Rookie of the Year and All-Star helped Florida toward the World Series championship in 2003.
Buckner was 0-3 with an 11.08 ERA in three starts for Arizona this season. The 26-year-old righty has spent four years in the majors.