Myers, who last year pitched out of the bullpen for the Chicago White Sox and Houston Astros, signed a deal that includes a club option for 2014, CBS Sports said.
The contract will reportedly become official once Myers passes a physical.
Myers, a converted starter, compiled 19 saves and a 3.52 ERA for the Astros before being obtained by the White Sox at the trade deadline.
He played eight years with Philadelphia, mostly as a starter, before becoming the team's closer in 2007.
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