Phil Mickelson, the 2013 Open champion, was one of the most high-profile players to feature in the opening LIV eventPlayers who have joined the Saudi Arabian-backed LIV Golf series will be allowed to play at The Open at St Andrews next month.
The PGA Tour suspended 17 members who played in the inaugural LIV Golf event, including Phil Mickelson and Dustin Johnson.
The European-based DP World Tour is expected to announce whether it will punish its rebels on Thursday.
The 150th Open will be played at St Andrews from 10-17 July.
"The Open is golf's original championship and since it was first played in 1860, openness has been fundamental to its ethos and unique appeal," said R&A chief executive Martin Slumbers.
"Players who are exempt or have earned a place through qualifying for the 150th Open in accordance with the entry terms and conditions will be able to compete in the championship at St Andrews.
"We are focused on staging a world class championship in July and celebrating this truly historic occasion for golf. We will invest the proceeds of The Open, as we always do, for the benefit of golf which reflects our purpose to ensure that the sport is thriving 50 years from now."
Exempt players are those who are eligible through their previously earned status, such as world rankings and tournament victories.
The PGA does not run the majors and so LIV golfers who would be allowed to play at the Open include Johnson, Mickelson, Bryson DeChambeau, Patrick Reed and Abaham Ancer, plus Brooks Koepka who is set to join the rebel series.
LIV Golf players were also permitted to compete at last week's US Open, which was won by England's Matt Fitzpatrick.
Like Fitzpatrick, defending Open champion Collin Morikawa has not joined LIV Golf, taking to social media on Tuesdayexternal-link to deny rumours he was planning to join the series.
Analysis
Iain Carter, BBC golf correspondent
The R&A had little choice but to allow the players to compete, even though the PGA Tour have handed out suspensions from their tournaments.
Entry criteria for the 150th Open was put in place long before the breakaway crisis developed and the Championship's essence is that it is "open" to all who are good enough to compete.
Whether that will be the case for future Opens remains to be seen because the R&A and United States Golf Association, who implemented the same policy at last week's US Open, are likely to want to remain close allies with the PGA Tour.
It is possible they could alter qualifying criteria for future events.
World rankings also play a key role in deciding eligibility for all majors. For rebel players hoping to compete in championships beyond this year, much might depend on whether LIV Golf's application for official ranking status is successful.
