Ponting, tormented after becoming the first Australian captain in 20 years to lose the Ashes last year, hammered an unbeaten 137 as Australia powered to 346 for three in the first Ashes Test against England on the first day at the Gabba on Thursday.
Ponting joined his predecessor Waugh as Australia's most prolific century-maker with 32 hundreds.
"I have no doubt he will finish as our best batsman after Bradman," Waugh wrote in a column in Sydney's Daily Telegraph on Friday.
"Averages now are probably five to seven runs higher than they used to be because boundaries have been brought in, but I still think Ricky is the most mentally tough batsman in the world at the moment," Waugh said.
"He has an insatiable appetite for runs and he knows how to get them."
The newspaper also acclaimed Ponting as Australia's best since Bradman.
"It is a grandiose tag worn by Neil Harvey, Greg Chappell and Allan Border as each man surged to deeds that made them standouts," the Daily Telegraph said.
"The latest always seems the greatest but there seems little doubt Steve Waugh's prediction for Ricky Ponting will come true. In fact he may be there already.
"Statistics are only part of what makes a great player, but if Ponting (59.13) continues on his current rampage, he will soon pass South Africa's Graeme Pollock (60.97) as the owner of the second-best batting average in Test history among the game's elite players.
The Australian newspaper agreed and said the captain may be embarrassed by the comparison but he is now in rare and exalted company.
Ponting has scored nine centuries in his past 12 Tests, an achievement matched only by Bradman among Australians.
West Indian Clyde Walcott once made 10 hundreds in 12 Tests and India's Sunil Gavaskar nine in 12.
Thursday's knock also took Ponting's tally to 32 centuries, equalling Waugh's total as the most by an Australian. India's Sachin Tendulkar (35), Gavaskar (34) and West Indian Brian Lara (34) are the only players with more.