The six-week tournament drew to a close with South Africa clinching their third world title by beating England in Yokohama.
France will host the event in 2023, with Beaumont also confirming that a dual bidding process will begin late next year for the 2027 and 2031 tournaments.
That would replicate the system used for 2015 and 2019, when England and Japan won staging rights.
And after the success of the sport’s first world cup in Asia, the door could be open for a strong bid from the United States.
“Japan 2019 will be remembered as probably the greatest Rugby World Cup,” said Beaumont, speaking at the tournament’s closing press conference in Tokyo.
“It has certainly been the most ground-breaking in terms of bringing the game to new audiences and attracting new fans to the sport.
“It has been amazing what we’ve experienced over the last six weeks, culminating in an outstanding final.
“As we look to the future, I can confirm that the World Rugby Council has approved the implementation of a dual host selection process for 2027 and 2031.
“The dual selection process will be launched in November 2020 and will enable World Rugby to select an optimal combination of hosts, rather like what we’ve achieved here.
“It will also give successful candidates longer preparation time to prepare and look at the costs and management of delivering tournaments.”
World Rugby chief executive Brett Gosper added: “Is this the greatest World Cup ever? Certainly the statistics would say that it is.
“More than 1.7 billion social media views – a world record television audience, 99 per cent stadium attendance, 1.2 million in the fan zones and possibly the largest digital sports event of 2019.
“It is the most competitive World Cup ever, with average winning margins between Tier One and Tier Two (teams) down.
“The average winning margin 30.5 (points) is a new low, there were Asian quarter-finalists (Japan) for the first time and very positive player welfare outcomes.”
Japan’s achievement in reaching the last-eight, beating Ireland and Scotland on the way, has brought calls for them to be allowed Rugby Championship or even Six Nations entry.
And Beaumont said: “There has been much talk about the future of the Brave Blossoms (Japan).
“We will do everything in our power to support them and all emerging teams to get regular access to high level competitions.
“Japan will have matches against England and Ireland in the next 12 months.
“We are looking at all our options. There is certainly an improvement in the Tier Two fixtures.
“I think there will be lots of movement, certainly within the next 12-18 months, around fixtures. The international calendar is something that is an evolving thing.”
An expansion of the World Cup from 20 to 24 teams has not been ruled out by World Rugby, although if that does happen, it would not be until 2027 at the earliest.
World Rugby’s chief operating officer Alan Gilpin said: “There are a number of questions that come from moving to 24 teams.
“How do we get the next four teams competitive? There are challenges there, and we are working on the high-performance programmes across a number of unions.
“The tournament is six weeks long, it is a big window in the international rugby calendar, and we don’t want to exceed that window. Going beyond six weeks would be challenging.
“It would not be for 2023, more the 2027 and 2031 process.”
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