His deal includes an invite to spring training.
San Diego signed the 31-year-old right-hander to a one-year, $2.5-million deal prior to the 2015 season and he went on to make just five starts for the club as he dealt with shoulder issues for much of the season.
Morrow underwent surgery in August to repair an impingement in his throwing shoulder.
The former first-round pick has made just 21 starts over the last three seasons, but comes with an impressive pitching repertoire when healthy.
He owns a record of 44-43 with an ERA of 4.22 and WHIP of 1.35, while striking out 9.2 hitters per nine innings pitched across his nine-year career.
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