The event will now take place next year.
Though exact dates have yet to be confirmed, organisers say it will not clash with the FIFA World Cup, which begins on November 21.
Organisers say the "extremely difficult" decision was taken by the boards of Rugby League World Cup 2021 (RLWC2021) - which includes representation from the Department for Digital, Culture, Media and Sport - and International Rugby League (IRL).
Players, competing nations, the Rugby League Players Association (Australia), UK government, hosts, commercial and broadcast partners were all consulted before the announcement.
Only three weeks ago, to mark 100 days until the opening match, organisers had insisted the tournament would take place.
However, the announcement Australia and New Zealand would not take part - and subsequent withdrawal of up to 400 players, match officials and staff from the NRL competition - dealt plans for this year a fatal blow.
Governing bodies in those nations had urged a postponement because of fears over player health and safety during the coronavirus pandemic.
Jon Dutton, the tournament's chief executive, said: “Today is a challenging moment for everyone involved in rugby league, but most importantly the players and fans of the competing nations.
“Ultimately, time and competing priorities from others forced us to make the most difficult decision in our six-year history.
"However, we and the sport of rugby league are resilient, and next year we will deliver our vision of the biggest and best Rugby League World Cup ever."
Dutton insisted: “We have always prioritised player voice and player choice.
"We have established a player working group, met with senior players and in the last few days commissioned a player survey to domestic players in Australia and New Zealand that showed more than 85 per cent wanted to compete at RLWC2021 this year.
"However, following the disappointing decision of the ARLC and NZRL to withdraw and the subsequent impact on player availability for other competing nations, it is apparent that delivering the tournament this year would not be feasible.
“The wellbeing of all those involved in the tournament, particularly players and team officials, has been our priority.
"I would like to thank the RLWC2021 board and my team for the relentless hard work and extraordinary measures that had been undertaken to create a safe and secure environment in line with other major sports events that have been successfully hosted in the UK this year.
“I would also like to thank all our committed partners as well as the rugby league community at large who have been so supportive of our trailblazing event.
"We appreciate the continued and unequivocal support of the UK government, as well as the understanding of our competing nations.”
Tournament chairman Chris Brindley added: “This process has shown that the RLWC board are responsible leaders who have put the solidarity and unity of the sport first.
"The board will now seek the commitment and alignment of all key partners immediately to deliver a clear timetable for the tournament next year.
“Now is the time for everyone who loves our game to come together, to show that rugby league deserves its place on the international stage, and that the RLWC is a tournament we can all be proud of.”
IRL chairman Troy Grant believes the delayed tournament will still be a success.
He said: “We must now move forward quickly from this point to build confidence in our sport internationally and to seize the opportunity which still presents itself; to deliver the best Rugby League World Cup ever.
"I look forward to 2022 and the future with optimism and a renewed focus on the importance of international rugby league for all our members large and small.
“We have seen the success that the Olympic Games and the Euro 2020 championship experienced after their postponements and we are all determined to deliver the best Rugby League World Cup ever in 2022.”
Sports Minister Nigel Huddleston said: “I am disappointed we've needed to take the decision to delay the Rugby League World Cup.
"Despite working tirelessly to explore solutions that would allow us to go ahead as planned, circumstances beyond our control have meant that postponing the Rugby League World Cup until next year is the strongest option for staging a successful tournament.
"In the best interests of the sport and its millions of supporters around the world, I look forward to the rugby league authorities in all competing nations accommodating a rearranged tournament in 2022, so we can put on the spectacle the fans deserve.”
Organisers say information on the rescheduling of the tournament and new dates will be released "in due course".