Meanwhile wicketkeeper Craig Kieswetter and all-rounder Samit Patel won recalls to both squads.
Kiewswetter replaced Matt Prior, England's Test gloveman who played at the World Cup.
Patel’s ability as a second spinner will enable England to field another slow bowler in addition to his county colleague Graeme Swann.
Fast-medium bowler Broad is expected to be fit to lead England for the first time at Bristol on Saturday despite bruising a heel during the drawn third Test against Sri Lanka at the Rose Bowl on Monday, a result that gave England the series 1-0.
England Test captain Andrew Strauss has retired from limited overs internationals so the one-day side will be led by Alastair Cook, even though his Test opening partner was not selected in the World Cup squad.
Meanwhile fast bowler Chris Tremlett, England's man of the Sri Lanka Test series, appears to have been rested ahead of the four Tests against India starting next month.
Twenty20 squad
Stuart Broad (captain), Ian Bell, Ravi Bopara, Jade Dernbach, Steven Finn, Craig Kieswetter (wk), Michael Lumb, Eoin Morgan, Samit Patel, Kevin Pietersen, Graeme Swann, Chris Woakes, Luke Wright
One-day squad
Alastair Cook (captain), James Anderson, Bell, Bopara, Broad, Dernbach, Finn, Kieswetter, Morgan, Patel, Pietersen, Swann, Jonathan Trott, Woakes
