Cox, made his international debut in England's T20I series against Australia last month, will fly head home to the UK after the end of the first day of the ongoing third and final Test against Pakistan in Rawalpindi before joining the white-ball tour of the Caribbean.
He is expected to be available for all three ODIs, but not the subsequent T20I leg as he prepares for the next Test trip to New Zealand.
Rehan, who is also in the playing XI of the ongoing Test against Pakistan, will join the white-ball squad at the end of the match.
In the absence of regular skipper Jos Buttler, who missed out due to a slight setback in rehabilitation from a calf injury, all-rounder Liam Livingstone will captain England in their upcoming ODI series against the West Indies.
England ODI and T20I squads: Jos Buttler (captain, T20Is only), Rehan Ahmed, Jofra Archer, Jacob Bethell, Jafer Chohan, Jordan Cox, Sam Curran, Will Jacks, Liam Livingstone (ODI captain), Saqib Mahmood, Dan Mousley, Jamie Overton, Adil Rashid, Phil Salt, Reece Topley, John Turner.