Zampa and Richardson, team-mates for Royal Challengers Bangalore, were expected home in Australia later on Thursday, a spokesman for the Australian Cricketers' Association (ACA) said, where they will undergo two weeks hotel quarantine.
There were concerns the pair would be stranded after the Australian government suspended passenger flights from India until May 15.
About 40 Australians remain involved in the IPL as players, coaches, officials and commentators, but Prime Minister Scott Morrison said they would not be allowed to jump the queue for repatriation flights when they resume.
The ACA said on Wednesday it was having "conversations" with Cricket Australia and the Australian government on how to repatriate cricketers from India at the end of the IPL.
"One thing I can tell you is our players are under no expectations to look for specific favours," ACA chief executive Todd Greenberg said on radio station 2GB. "There's no free rides or any expectations from our players. What they are looking for is the right information so they can plan accordingly."
The regular IPL season ends on May 23, with playoffs to follow before the final on May 30.
Andrew Tye was the first Australian to leave the tournament and he arrived back in Sydney earlier this week.
Zampa and Richardson can expect to feature in Australia's limited-overs tour of West Indies with the squad due to depart in late June for a trip that includes three ODIs and three T20Is.
For the remaining players IPL-based who will feature on that tour, currently there is a 26-day period from the end of the IPL to when the squad departs with 14 of those being needed for quarantine in Australia.
"We're monitoring it almost daily. There's no doubt about that," head coach Justin Langer told Fox Cricket's Road to the Ashes show. "As it stands now, the guys will come back about 26 days before we're supposed to leave for the West Indies tour, so we'll be watching it closely."