Morgan, who was due to captain a World XI against West Indies this week but had to pull out of that Hurricane Relief Twenty20 at Lord's, will as expected take charge of England on June 10 against Scotland and then in five Royal London Series matches against Australia.
The Irishman was named on Wednesday morning in a 13-man squad to travel to Edinburgh - from which Jos Buttler will be rested - and then one of 14 against Australia in a series starting at The Oval on June 13.
Sam Billings will be included against Scotland to deputise for wicketkeeper Buttler, and seamer Tom Curran will bolster the squad by one when he is added to the ranks to face Australia.
Morgan chipped a bone in his finger while fielding for Middlesex last weekend but after scans was reassured by medics that his England availability would not be affected.
In a predictable line-up for the International Cricket Council's number one-ranked 50-over team, Alex Hales retains his position as an option at the top of the order - while there is no place yet for Dawid Malan, who is still uncapped in this format.
Hales made a half-century, in the absence of the injured Jason Roy, in England's last ODI - a seven-wicket victory over New Zealand in Christchurch to clinch a 3-2 series success in March.
Buttler's one-match rest is "on the recommendation of the captain and coach", the England and Wales Cricket Board explained in a brief press release.
England squad v Scotland: EJG Morgan (Captain), MM Ali, JM Bairstow, SW Billings (wkt), AD Hales, LE Plunkett, AU Rashid, JE Root, JJ Roy, BA Stokes, DJ Willey, CR Woakes, MA Wood
England squad v Australia: EJG Morgan (Captain), MM Ali, JM Bairstow, JC Buttler (wkt), TK Curran, AD Hales, LE Plunkett, AU Rashid, JE Root, JJ Roy, BA Stokes, DJ Willey, CR Woakes, MA Wood
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