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Vargas will pitch the second game of the season against the Tigers, the Kansas City Star reports.
Vargas signed a four-year, $32 million contract with the Royals on Thursday, Jeff Passan of Yahoo! Sports reports.
The Angels are unlikely to extend Vargas a qualifying offer for the 2014 season, the Los Angeles Times reports.
Vargas (9-8) allowed four runs (three earned) on seven hits in 6.1 innings pitched in a loss to the Rangers Sunday.
Vargas went the distance without allowing a run in a win against the Athletics on Tuesday, allowing four hits and striking out five in the contest.
Vargas allowed four runs on seven hits in six innings of work, picking up a no-decision against the Athletics on Wednesday.
Vargas was hit hard by the Astros on Friday, giving up eight runs on nine hits in just 4.1 innings pitched to fall to 8-7 on the season.