Joshua was named on Dale's bench for their EFL Trophy tie at Hartlepool in November and was also given an honorary player of the month award by the EFL.
After he was too ill to attend the game, players visited him in hospital to present his personalised shirt.
Rochdale have also retired the number 55 that they registered for Joshua.
"Staff at the club first met Joshua last year and he touched the hearts of everyone," said a club statement.
"Our thoughts are with his mum Nicola and his dad Kevin at this very difficult time. We send Nicola, Kevin and their family our sincerest condolences and love.
"We will continue to offer our support to the family at this time."
Rochdale boss Keith Hill said Joshua's story had "touched the hearts" of everyone after the team first met him in February.
League One side Rochdale have announced that five-year-old supporter Joshua McCormack has died after his battle with a brain tumour.