Australia also remain the top-rated one day international side in the latest official rankings from the International Cricket Council (ICC).
It is the first time since December 2008 that Australia have been ranked number one in Tests and ODIs at the same time. They last held the top Test ranking in August 2009, when they were displaced after losing the Ashes 2-1 to England.
Darren Lehmann's Australians nudged out South Africa, who had held the top Test spot since August 2012.
England are currently third, ahead of Pakistan and India.
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Australia captain Michael Clarke said he was delighted with the turnaround in his team's fortunes.
"We are incredibly proud to be the number-one ranked team in the world in both Test and ODI cricket, which are two of the team's most important goals," Clarke said.
"There has been an enormous amount of hard work and effort on and off the field that has led to this result.
Lehmann has turned around the fortunes of the Australian Test and one-day sides following a tumultuous period in which coach Mickey Arthur was sacked.
After losing the 2013 Ashes series 3-0 in England, Australia swept their return home series against England 5-0 during the last southern summer.
They then scored an impressive 2-1 away series win over South Africa.