The host country for the tournament will be decided in Autumn by the RLIF.
The RFL are targeting to reach one million spectators for the 201 World Cup.
“The RLWC 2021 provides an ideal opportunity for the nation to demonstrate again to a global audience its ability to stage a world-class sporting event we can all be proud of,” RFL chairman Brian Barwick said.
“It will top off a superb decade of incredible sporting events held in this country that began in 2012 with the London Olympics.”
The Government has pledged £15 million to stage the tournament and an additional £10 million provided to the RFL for Rugby League Infrastructure in the North of England.
“The UK is proud to have delivered some of the most memorable major sporting events in recent history including the hugely successful 2013 Rugby League World Cup,” Secretary of State for Culture, Media and Sport, John Whittingdale MP, said.
“We now want to build on the success of 2013 by hosting the competition once again in 2021.
“The government’s support for the RFL’s bid will help put on a larger tournament that not only brings economic benefits to host towns and cities in Rugby League’s heartland, but promotes the sport to a wider audience both nationally and around the world.”