Cullen penned a loan contract at City this Thursday which will keep him at the Coral Windows Stadium initially until March 12.
The central midfielder will wear squad number 12 during his time at Valley Parade.
Speaking about Cullen's arrival, Bantams boss Phil Parkinson said: "We are delighted to have Josh on board.
"He has signed his paperwork and trained with the lads today (Thursday), and we look forward to working with him.
"Obviously we have Reece (Burke) here on loan from West Ham already and we hope that Josh can settle in just as well as he has.
"Josh has been in and around the first team environment at West Ham and has been on the bench several times so he is mature for his age. He goes straight into the squad for Saturday (vs Peterborough United)."
After featuring twice as an unused sub last season in West Ham's Premier League games at Arsenal and Aston Villa, Cullen made his senior debut for the Hammers last July in their UEFA Europa League qualifier with FC Lustians.
The 19 year-old made three appearances in total for West Ham in Europe over the summer.
Fellow Bantams loanee Reece Burke also featured for West Ham in their Europa League campaign alongside Cullen.
Cullen made his Premier League debut as a late substitute in West Ham's 3-0 win at Liverpool at the start of this season.
He also has five caps to his name at Under 21 level for the Republic of Ireland, the most recent of which came in November against Lithuania.