Paine stepped down from the post on Friday after being investigated by Cricket Australia (CA) for sending explicit messages to a female co-worker in 2017.
Warne feels Cummins, who is the current vice-captain, should be named the captain immediately ahead of the Ashes series.
“For me, the time is right to make Pat Cummins captain, something I thought even before the events of Friday unfolded,” Warne wrote in Australia’s The Daily Telegraph.
The 28-year-old Cummins, who made his debut in 2011, has snapped 164 wickets in 32 Tests.
“The poster boy, respected and loved the world over, Pat Cummins should now be named captain, and either Matt Wade, Josh Inglis or Alex Carey should get their chance to come in and play Paine’s role in the Test team.”
Warne singled out that Inglis is a “360 degree player” and would be the right man for the wicketkeeping job.
“Inglis gets my vote. He’s got silky smooth hands behind the stumps, he’s a 360 degree player with the bat and coming off three first class hundreds last season for Western Australia,” he wrote.
“He’s a great team man who I saw first hand at the London Spirit this year. He’s 26. Get him in.”
The former leg-spinner also empathised with Paine, saying he is just human and shouldn’t be judged.
“It was sad to see what happened last Friday on so many levels and the circumstances in which Tim was forced to stand down. I really feel for him, what he’s going through, and what his family is going through,” Warne wrote.
“I’m not judging him on this incident. Just because Tim is in the public eye doesn’t mean he won’t make a mistake. Sportspersons are human, they have feelings. Let’s stop the judgement. It’s not our place to do that.”
The Ashes begins with the first Test at Brisbane on December 8.