Wood has returned to fitness after being sidelined for several months following a third ankle operation.
The Durham seamer has done enough in the opening weeks of the season to persuade the England selectors he is ready for the tournament, which will be held in England and Wales in June.
England regard the eight-team event as a chance to land a first global 50-over trophy and Wood is a potentially key performer.
There are no real surprises in the squad, which will also take on South Africa in a three-match series before the Champions Trophy, but Finn might have hoped to oust one of Jake Ball or David Willey from the party.
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The Middlesex man played all three matches in England's last 50-over series, against the West Indies but Willey offers variation as a left-armer and with Ball arguably a more consistent like-for-like option, there is no place for the paceman.
Liam Plunkett has yet to play this season due to a calf injury but he is closing in on a return and, with the International Cricket Council permitting changes up to May 24, he has been given the nod.
England's season will begin with the games against Ireland at Bristol and Lord's on May 5 and May 7, with Ben Stokes, Jos Buttler and Chris Woakes all excused as they continue their Indian Premier League adventure.
Captain Eoin Morgan, wicketkeeper-batsman Sam Billings and opener Jason Roy will report back from India for those games, with Finn and Northamptonshire batsman Ben Duckett selected as cover.
England squad for Ireland series: Eoin Morgan (Middlesex, capt), Moeen Ali (Worcestershire), Jonny Bairstow (Yorkshire), Jake Ball (Nottinghamshire), Sam Billings (Kent), Ben Duckett (Northamptonshire), Steven Finn (Middlesex), Alex Hales (Nottinghamshire), Liam Plunkett (Yorkshire), Adil Rashid (Yorkshire), Joe Root (Yorkshire), Jason Roy (Surrey), David Willey (Yorkshire), Mark Wood (Durham).