Finch who played his first matches for Australia since sustaining an injury during the IPL and he displace Joe Root, who was rested for the ODI series, at the No 10 spot.
Australia beat England by eight wickets in their fifth and final one-day international at Old Trafford, Manchester on Sunday to win the series 3-2.
England captain Eoin Morgan retired hurt with concussion after he was hit on the head by a Mitchell Starc bouncer in the final one-day international against Australia at Old Trafford.
Eoin Morgan inspired England to their best one-day international run chase against Australia as they levelled the five-match series to set up a decider at Old Trafford on Sunday.
James Taylor's maiden one-day international century helped England keep the series alive as they beat Australia by 93 runs at Old Trafford, Manchester on Tuesday.
Batsman-wicketkeeper Peter Handscomb and one-test all-rounder John Hastings have been called into Australia's injury-hit squad for the remainder of the one-day international series against England.
Jonathan Bairstow will replace Jos Buttler in England's squad for the final three matches of their one-day international against Australia.
Australia will head to Old Trafford with a 2-0 lead in this series after their 64-run win over England at Lord's.
Matthew Wade's unbeaten 71 laid the platform for World Cup-holders Australia's 59-run win over England in the first day/night one-day international in Southampton on Thursday.
Virat Kohli has eclipsed Aaron Finch as the number-one ranked batsman in the latest ICC T20 player rankings, which were released on Tuesday.
