To make room for Drake on the 40-man roster, right-hander Mark Leiter Jr. was designated for assignment.
Drake, 33, pitched for five teams in 2018, including a brief stint with the Blue Jays in early August. In 47.2 innings with the Brewers, Indians, Angels, Blue Jays and Twins last season, Drake had a 5.29 ERA with 51 strikeouts and 17 walks. The Rays claimed Drake off waivers from the Twins on Nov. 1.
Leiter, 27, was selected off waivers by the Blue Jays from the Phillies on Sept. 1. In 6.2 innings with the Jays, he had a 13.50 ERA with four walks and nine strikeouts.