England beat Australia by 48 runs in their curtain-raiser at Edgbaston last Sunday without Swann, who was suffering from a back from problem.
But the Nottinghamshire spinner, who took eight wickets against Sri Lanka when they toured England in 2011, trained with his team-mates on Wednesday morning and is expected to be fit enough to replace James Tredwell in the side.
"Swanny is fit," England captain Alastair Cook said. "His injury was a strange one. He must have jarred his back in training and woke up with a stiff back the next day. That can happen but at the moment he is back and available for selection."
England took first blood in their long battle with old foe Australia last Saturday as they cruised to victory thanks to 91 from Ian Bell and three wickets from James Anderson.
The performance was a marked improvement on the team's efforts earlier this summer when they fell to a shock 2-1 ODI series defeat against New Zealand. Cook now believes his team are back on track, which bodes well ahead of a crucial seven months for English cricket.
"The win against Australia was a good one, as was the last one against New Zealand," the England skipper added.
"The first two games against New Zealand (where England lost at Lord's and at the Rose Bowl), seem to be out of the way. We seem to have recovered a bit of form and confidence now. It's a vitally important game tomorrow, we can make a really big stride towards the semi-finals if we win."
Other than Swann's return, England are unlikely to make any changes to their team.
Cook has confirmed that batsman Joe Root will play despite being the intense spotlight that has fallen on him since he was punched by Australia's David Warner in a Birmingham bar in the early hours of Sunday morning.
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