The 25-year-old Dublin-born Morgan, the vice-captain of England's Twenty20 team, played in the 2007 World Cup for Ireland before shifting to England so that he could play Test cricket.
Morgan, who made his England debut two years later against West Indies, hit four ODI centuries, one of these for Ireland.
He will be the second Irishman to captain England, the first being Frederick Fane in an Ashes series in the 1907-08 Ashes series down under.
Jonathan Bairstow, James Taylor, Scott Borthwick and Ben Stokes are the uncapped players in the 13-member squad. The four had impressive outings for England Lions that beat Sri Lanka 2-1 in a three-match one-day series.
Taylor, 21, in particular has been in good form, scoring two centuries. Wicketkeeper Bairstow, 21, the son of former England player David Bairstow, Durham batsman Stokes, 20, and his county-mate and legspinner of promise, Borthwick, 21, will be watched with keen interest.
Also in the squad is Jonathan Trott, who missed the last two Test matches against India with a shoulder injury. Regular ODI captain Alastair Cook, Kevin Pietersen, Ian Bell, Stuart Broad, Graeme Swann and James Anderson have all been rested.
Ireland scored a sensational victory over England at the World Cup in the subcontinent earlier in the year.
The squad:
Eoin Morgan (captain), Jonathan Bairstow, Ravi Bopara, Scott Borthwick, Jade Dernbach, Steven Finn, Craig Kieswetter, Graham Onions, Samit Patel, Ben Stokes, James Taylor, Jonathan Trott, Chris Woakes.
Eoin Morgan second Irish to lead England
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