Dwayne Bravo, Kieron Pollard, Sunil Narine and Marlon Samuels are others who could also be available.
West Indies' policy has been to only select players if they feature in the same format in domestic cricket.
And many have chosen not to play in West Indian one-day competitions.
That is because they often clash with lucrative overseas leagues such as the Big Bash.
The West Indies will travel to England next month, beginning a three-match Test series with a day-night match at Edgbaston on 17 August.
The squad for that series will be missing a host of big names as it has already been selected.
Following the Test series, the teams will meet in a Twenty20 match at Chester-le-Street on 16 September before the first of five one-day internationals at Old Trafford on 19 September.
In a statement, Cricket West Indies (CWI) said the "amnesty" with the players' union was "part of a wider strategy to be more inclusive and to improve player relations".
In 2014, a tour of India ended abruptly because of a dispute over pay, while the West Indies missed out on qualifying for the Champions Trophy earlier this year.
"We recognise that it is highly unlikely that we will now automatically qualify for the 2019 World Cup," said CWI chief executive Johnny Grave.
"So whilst the qualifying tournament has yet to be confirmed by ICC, we may only have eight ODIs against England and New Zealand in the next six months to prepare.
"It is crucial that we can have our best-performing Windies players available for selection in these important games."
Chris Gayle is among the West Indies players who could now play in this year's one-day series in England after a "temporary amnesty" between their union and the team's cricket board.