Revere can immediately slide into left or center field for Washington and bat leadoff in front of new addition Daniel Murphy and NL MVP Bryce Harper.
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Revere, 27, batted .306/.342/.377 and swiped 32 bases in 152 games between the Phillies and Blue Jays in 2015.
Storen, 28, logged 55 relief innings for the Nationals last season with a 3.44 ERA.