Clarke missed Australia's entire Champions Trophy campaign in June due to a flare-up of the injury, and felt some discomfort early in the failed Ashes campaign.
England have rested a host of their top players for the five-game series, starting in Leeds on Friday, but Clarke said he never considered going down the same path.
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The 32-year-old is desperate for success and says he views the series as just as important as any other.
"It was a no-brainer for me if I wanted to stay here and play the one-dayers," Clarke told reporters at Headingley on Thursday.
"I want to play every game I can for Australia.
"I'll prepare today, as I have done over the past few days, like I would if it was the first Test of the Ashes. It's just as important to me."
"I think it's important I'm here with the team and performing and leading from the front.
"I want to see this one-day team back to where it belongs - at the top of the tree."
Clarke said he had no issues with his back heading into the series.
And he dismissed suggestions he could consider giving up the 50-over format in the near future to preserve his Test career.
Clarke has already dropped international Twenty20 in a bid to lighten his load but he is focused on leading Australia to the 2015 one-day World Cup.
"I think it's obviously manageable," he said of his injury.
"I feel as fit and strong as I have throughout my career.
"I can't see any reason why I can't continue to manage it and play for a lot longer in both forms of the game."