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Morrow had a 2.73 ERA in 33 innings over his first five starts before he landed on the disabled list on May 5 with inflammation in his right shoulder.
Morrow had his rehabilitation trail halted by a setback during the summer, which eventually led to surgery in mid-August to repair an impingement in the shoulder.
The stated recovery period at that time was 3-4 months, meaning that he should be ready for the start of Spring Training in February.
Morrow last appeared in a big league game on May 2, and he suffered two setbacks -- one on June 7 with Double-A San Antonio and another on July 25 with Triple-A El Paso -- as he attempted to get back to the big leagues.
Finally, in August, Morrow elected to have surgery.
Morrow, 31, gives the Friars another starting option heading to Spring Training, as the Padres will likely still look to add a starting pitcher to pair with Tyson Ross, James Shields and Andrew Cashner. There are several internal candidates as well.
Morrow, who has appeared in 236 big league games in his career, will not be the only one in camp on a Minor League deal with Major League service time.
The Padres have signed right-handed pitcher Phillip Humber, who will turn 33 on Dec. 21, to a similar deal.
Humber hasn't pitched in the big leagues since 2013. He spent '14 with the A's Triple-A team in Sacramento before pitching in Korea last season.
Humber, of course, is best known for tossing a perfect game in April 2012 against the Mariners while pitching for the White Sox.
The Padres have also signed 35-year-old catcher Erik Kratz to a Minor League deal with a Spring Training invitation, as well as left-handed pitcher Ryan Buchter.
Kratz has played for the Phillies, Royals, Pirates and the Blue Jays over parts of six seasons (2010-2015).
Buchter, 28, tossed one scoreless inning of relief for the Braves in 2014. He has a 1.30 ERA this winter with 45 strikeouts in 27 1/3 innings for Culiacan of the Mexican Pacific Winter League.