Jordan is already in Australia with the one-day international squad where he has shown signs of promise despite England going 2-0 down in the five-match series.
Middlesex quick Finn was the only member of England's originally selected Ashes squad who didn't play an international match on a tour where his side were routed 5-0 by Australia in the Test series.
He returned home early in a bid to iron out problems with his bowling action which England limited overs coach Ashley Giles said had made him "not selectable".
Finn's problems mean he is unlikely to make it into England's squad for the World Twenty20 in Bangladesh in March, even though he was named this week in the provisional 30-man party.
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Jordan, yet to play a Twenty20 international, was also selected in that provisional squad but will now have a chance to show what he can do in cricket's shortest format.
England's one-day series against Australia continues in Sydney on Sydney.
After the ODIs, Australia and England play three Twenty20 internationals, with matches in Hobart (January 29), Melbourne (January 31) and Sydney's Olympic Stadium (February 2).