Selectors said they were acting on medical advice to rest Ponting, who has a sore back, and wicketkeeper-batsman Gilchrist from making the trip to New Zealand for the three limited-over matches.
Hussey will captain the 13-man squad with batsman Michael Clarke his deputy.
Selectors have brought in young West Australian batsman Adam Voges and New South Wales wicketkeeper Brad Haddin as their replacements for the matches on February 16, 18 and 20.
"We have received medical advice that it would be prudent for Ricky Ponting to withdraw from competitive cricket in between the tri-series finals (against England) and the start of the ICC World Cup," chairman of selectors Andrew Hilditch said Friday.
"While his sore back does not prevent him from playing cricket at present, we are advised that for Ricky to arrive at the World Cup in the best possible physical shape, his workload should be managed through this period," he said.
"There is no question over Ricky's availability for the World Cup."
Hilditch said Gilchrist should also have a rest before the World Cup in the Caribbean starts on March 13.
"Adam Gilchrist has had a demanding summer and has performed brilliantly in both forms of the game," Hilditch said.
"It is felt that he should use the period after the tri-series finals to allow his body to properly recover in advance of the World Cup. Both these decisions have given Brad Haddin and Adam Voges an international opportunity."
Hussey captained the Australian team at the DLF Cup in Malaysia ahead of last year's Champions Trophy in India.
"It is a great honour to be selected as the captain of Australia in Ricky's absence," he said. "I am looking forward to going over to New Zealand and we are aiming to claim the Chappell-Hadlee Trophy."