Both finals will take place back to back on 19 November 2022, with the wheelchair final to be staged a day earlier at the Manchester Central convention centre.
It will now take place between 15 October and 19 November next year.
Old Trafford was already scheduled to host the men's and women's finals, but the wheelchair final had originally been set to take place at the M&S Bank Arena in Liverpool - which is unavailable to stage the rearranged match.
That is one of five games to have moved venues as a result of the year-long postponement.
In the men's tournament, the match between holders Australia and Fiji on the opening day will now take place at Headingley, Leeds, as a result of a clash with another event in Hull.
In return, the MKM Stadium, Hull, will host New Zealand v Jamaica in Group C on 22 October - a fixture that was scheduled to be played in Leeds.
Anfield, which was set to stage a women's match between England and Canada and a men's quarter-final, is no longer available as a result of expansion work at Liverpool FC's stadium.
Those matches will now be held at Wigan's DW Stadium on 5 November.
England will still open the tournament with a group game against Samoa at St James' Park, Newcastle, on 15 October while Headingley will open the women's competition on 1 November.
A double-header at the Copper Box, London, will kick-off the wheelchair event on 3 November.
All 61 games will be shown live on BBC channels.
A total of 32 teams across 21 competing nations will participate in the men's, women's and wheelchair events.
RLWC2021 chief executive Jon Dutton said: "We have achieved our objective in delivering minimal disruption to the existing 61-match schedule and I want to place on record my thanks to all those who have made it possible.
"Every host town and city who joined us on this journey remains involved and they will set the stage for the very best that the sport has to offer. There are world-class, compelling matches, across all three tournaments at some of the most iconic venues across England."