Padraig Harrington and Steve Stricker have welcomed the event's postponement for 12 months.
The biennial contest between the United States and Europe will now be held at Whistling Straits in September 2021 and every two years thereafter.
Continuing concerns over coronavirus meant the Wisconsin venue was unable to host fans this year – a scenario both captains, plus organisers and the majority of players likely to be involved, were not in favour of.
However, the PGA of America has warned if the 2021 Ryder Cup cannot proceed as they would envisage it would most likely be cancelled next year.
"When you think of the Ryder Cup you think of the distinctive atmosphere generated by the spectators, such as around the first tee at Le Golf National two years ago. If that cannot be responsibly recreated at Whistling Straits in September, then it is correct that we all wait until it can be." -- Padraig Harrington
"Rescheduling the Ryder Cup was never going to be an easy decision given the many factors to take into consideration but I believe it is the right assessment given the unprecedented circumstances we are facing at this time," said European captain Harrington.
"When you think of the Ryder Cup you think of the distinctive atmosphere generated by the spectators, such as around the first tee at Le Golf National two years ago.
"If that cannot be responsibly recreated at Whistling Straits in September, then it is correct that we all wait until it can be.
"I know, right now, that September 2021 feels like a long time away but it will come around quickly and I guarantee that the European players and I will be ready when it does."
American counterpart Stricker, born and still a resident in Wisconsin, was in agreement, saying: "At the end of the day, we want to stage a Ryder Cup that will rival all other Ryder Cups in my home state of Wisconsin, and now we have the opportunity to showcase the event as it was meant to be seen."
PGA of America chief executive Seth Waugh stressed public safety was paramount in their decision-making
"Given that uncertainty, we knew rescheduling was the right call. As disappointing as this is, our mandate to do all we can to safeguard public health is what matters most," he said.
The Ryder Cup's move to September 24-26, 2021 means the Presidents Cup at Quail Hollow Club in Charlotte, North Carolina, will now be played the following September.
The European Tour has confirmed that the qualification process for Team Europe for the 43rd Ryder Cup has been frozen until the beginning of the new year, with all points earned to date on both the European and World Points lists continuing to count.
Officials are looking into the potential for 'points multipliers' to be introduced during the 2021 season to ensure the performances of in-form players are given the relevant importance.