To make room on the 40-man roster Wednesday, the Brewers designated right-hander Michael Blazek for assignment.
Franklin is expected to report to the Brewers on Friday when they open a three-game series against the Chicago Cubs. At that point, a player will need to be trimmed from Milwaukee's 25-man roster.
Franklin was drafted 27th overall by Seattle out of high school in 2009. He hit .270 with six home runs and 26 RBI in 60 games last season for the Rays. For his career, the switch-hitter has batted .219 with 22 home runs and 84 RBI in 234 games.
Blazek was optioned to Triple-A Colorado Springs this spring. He was 3-1 with a 5.66 ERA in 41 games for Milwaukee last season.