Arthur, who coached South Africa from 2005 to 2010 before taking over the reins with Australia last year, sang the praises of the Tasmanian in his blog on the Cricket Australia website, making special mention of his preparation, teamwork and character.
"Over the last 18 months I've had the pleasure of sharing the dressing room with Ricky in my time as coach of the Australian team," Arthur said. "(Ricky is a) tireless worker (and) the best 'team man' I have ever seen."
He added: "I've quickly learned that Ricky is the ultimate professional - the most proficient player I have ever coached - and someone that everyone in the dressing room listens to and learns from every time he speaks.
"Not only do his batting stats prove that he is Australia's best since [Don] Bradman, but he revolutionised fielding and leaves international cricket as Australia's most successful captain.
"He departs international cricket as one of Australia's all-time greats and leaves a lasting legacy. He will be sorely missed. Ricky Ponting will leave a massive hole in the Australian team dressing room."
Ponting called time on his Test career last week, finishing with 13,378 runs - which came at an average of 51.85 and included 41 centuries - from 168 matches.
The 37-year-old, who held a long-standing desire to play the Ashes in England next year, retired earlier than he would have liked after a poor run of form against South Africa.
Despite a stellar start to the Sheffield Shield season, Ponting failed to convert his form onto the international stage and was denied a fairytale ending to his career that many would argue he deserved. But Arthur says despite a lack of runs against South Africa, his presence around the group was invaluable.
"From an outsider's perspective, it could be argued that perhaps his numbers in the recent series against South Africa weren't as high as he would've liked, but despite that, Ricky offered a whole lot more than just a magnitude of runs," he said.
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