The England-based pair reinforce a squad that has lost opening batsman David Warner, all-rounder Shane Watson and paceman Nathan Coulter-Nile to injuries in recent days.
The 24-year-old Handscomb, an opening batsman yet to be capped in international cricket, has been playing for English county side Gloucestershire.
Hastings, 29, has padded up for Durham and returns to the one-day squad four years after the last of his 11 ODIs against Sri Lanka in Colombo.
The pair's call-up follows the inclusion of Yorkshire-based opener Aaron Finch to replace Warner on Saturday.
"We looked at all options including the possibility of flying in cover from Australia but the fact all three of the players we have drafted in are already in England means they can join us at short notice, be acclimatised to conditions and be available for selection immediately, if required," Australia coach Darren Lehmann said in a media release.
"We look forward to them playing their parts in trying to ensure we finish this tour with a victory in the one-day international series against England."
Australia will bid to seal the five-match series in the third game in Manchester on Tuesday.
(Reporting by Ian Ransom; Editing by Greg Stutchbury)
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