The deals include invites to spring training camp, where the defending AL Central champions must address two glaring issues - outfield depth and their bullpen. Joyce and Wilson agreed to their deals on Friday, pending medical exams which were completed Saturday.
Joyce spent the past two seasons with the Oakland Athletics. The 34-year-old hit 25 home runs and drove in 68 runs in 2017, but was limited to 83 games last season because of lower back problems. Joyce was an All-Star in 2011 for Tampa Bay.
If he makes the Indians' 40-man roster, Joyce will make $1.25 million next season while in the majors and he can earn $500,000 in performance bonuses.
The 32-year-old Wilson pitched in 59 games for Detroit last season, posting a 3.36 ERA. He limited right-handed hitter to a .191 average. Wilson has spent the past four seasons with Tigers.
Wilson will also get $1.25 million if he makes the roster and can get another $750,000 in bonuses.
Cleveland is rebuilding its bullpen following the departures of closer Cody Allen and left-hander Andrew Miller.
The Indians have 19 non-roster invitees coming training camp, which opens for pitcher and catchers on Feb. 12 in Goodyear, Arizona.
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