Collingwood and Pietersen have both being playing in the IPL
England will fly direct to the West Indies from Gatwick on Sunday for the third ICC World Twenty20 tournament.
Alternative plans, including the possibility of sea and land travel, had been explored because of the crisis caused by the Icelandic volcano.
But the England and Wales Cricket Board told BBC Sport that such contingencies were no longer necessary.
And the International Cricket Council confirmed all teams will now revert to their original travel schedules.
England, one of eight teams yet to travel to the Caribbean for the 12-team tournament, could have flown from Dubai, if their scheduled flight from London had remained grounded because of the volcanic ash cloud produced by an eruption in Iceland.
But that would have meant an arduous trip by sea, train and probably air east to the United Arab Emirates - in the wrong direction - before flying back across Europe and the Atlantic to Barbados.
ICC sponsors Emirates Airlines had agreed to provide a charter-flight contingency for teams, essential back-up staff and broadcast crews.
"I'm delighted to say that the teams will now fly to the West Indies as originally scheduled. I want to thank both Emirates and the ICC executive for working so hard to ensure that we had a back-up plan to transport teams to the Caribbean," said ICC chief Haroon Lorgat.
The only remaining complication for England is the individual travel arrangements of squad members recently involved in the Indian Premier League.
Captain Paul Collingwood, who played his last match for the Delhi Daredevils on Sunday, was still in India as of Tuesday but is expected to join up with the squad before Sunday's flight to the Caribbean.
Ravi Bopara last played for Kings XI Punjab on 7 April and is also scheduled to fly with the main party.
After his Bangalore Royal Challengers side's semi-final defeat to Mumbai Indians on Wednesday, Kevin Pietersen faces a third-place play-off on Saturday. He may then make his way to the West Indies directly from India.
Team-mate Eoin Morgan, however, was not in Bangalore's squad for the semi-final and is now in Dubai for a short break, according to the Professional Cricketers' Association.
Michael Lumb did not play in Rajasthan Royals' final match on 17 April but is also set to fly straight from India to the West Indies to join up with the England squad.
England are due to play a warm-up game against Bangladesh in Barbados next Wednesday and another against South Africa the following day, before beginning the tournament proper on 3 May against hosts West Indies in Guyana.
Ireland and Zimbabwe are already in the Caribbean, having recently played one-day fixtures against West Indies, while New Zealand are travelling via the United States, and are not affected by European air restrictions.