Opening batsman Cook, England's all-time leading Test run-scorer, resigned as skipper in February after a 4-0 series loss in India late last year following 17 series in charge.
Joe Root succeeded Cook with dynamic all-rounder Ben Stokes his deputy.
"It's a very exciting time," Cook told Sky Sports on Wednesday. "It's kind of the next generation of leaders, obviously with Ben as well, pushing that team forward.
"I hope I can score enough runs to justify my place at the top of the order."
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During England's victorious 2010/11 Ashes tour under Andrew Strauss he scored a mammoth 766 runs, including three hundreds, at an average of 127.66.
But as captain Cook presided over England's 5-0 series loss in 2013/14, where he managed just 246 runs at 24.60.
"As players you'd love to get on that plane and be part of an Ashes squad," said Cook, who also led England to home Ashes series wins in 2013 and 2015.
"I've had some pretty dark moments as a player (in Australia) but also a very special tour in 2010/11, which is repeatable."
"Australia at home will be favourites -- they're a very hard side to beat at home -- but if you look through our team now there's a lot of strength there."
Cook is convinced he quit the captaincy at the right time after the India whitewash.
"I was pretty clear, leaving that tour, that my race was run as captain," he said. "I felt the team needed a change of voice, a change of direction.
"We lost too many games (in 2016) for the talent we've got in that side.
Cook had hoped to play in Essex's County Championship opener against Lancashire starting on Friday.
But earlier on Wednesday England and Wales Cricket Board (ECB) said he had been ruled out of the match with a hip injury.
His absence is understood to be a precaution against aggravating an injury which is not thought to be serious at this stage.
The match would have seen Cook and Lancashire paceman James Anderson, England's leading Test run-scorer and wicket-taker respectively, in opposition.
"Cook has been receiving treatment for the problem for several weeks. A scan this week has ruled out serious injury, but he will undertake an injection in the upcoming days to help settle his symptoms," said an ECB statement.
No longer involved in international limited-overs cricket, Test specialists such as Cook are not due to represent England again until the opening match of the South Africa series at Lord's on July 6.