Yorkshire leg-spinner Rashid and Durham seamer Wood are currently on tour with England in the West Indies but were not selected for any of the Test matches.
And, with the third and final Test now underway, the duo will return early from the Caribbean and link up with the rest of the 13-man squad ahead of Friday???s game in Malahide, near Dublin.
Nottinghamshire batsman James Taylor will captain a new-look England side which is certain to feature some new faces.
Zafar Ansari, Sam Billings, Lewis Gregory, James Vince, David Willey and Wood are all in contention for senior international debuts.
England ODI squad to play Ireland: James Taylor (captain, Nottinghamshire), Zafar Ansari (Surrey), Jonathan Bairstow (Yorkshire), Sam Billings (Kent), Tim Bresnan (Yorkshire), Steven Finn, Lewis Gregory (Somerset), Alex Hales (Nottinghamshire), Adil Rashid (Yorkshire), Jason Roy (Surrey), James Vince (Hampshire), David Willey (Northamptonshire), Mark Wood (Durham)