The ex-Sheffield Eagles, Hull and Wakefield Trinity boss' departure was announced on Tuesday, less than 24 hours after a 32-18 home defeat by Featherstone Rovers which left Bulls ninth in the Championship table.
That was their fifth defeat in nine league games this season.
Bulls chairman Nigel Wood told the club's website: “We would like to thank John for his considerable efforts on behalf of the club over the last four years.
"We met this morning and both agreed that it was in the club’s best interests to make a change at this moment in time.
"On a personal basis, I am very pleased for John, in what turned out to be his final match as head coach, that our performance last night was full of character and resilience. He leaves with our best wishes”.
Kear was quoted as saying: “Having been at the Bulls for four and a half years, I feel that this move is the best one in order to take the club forward.
"I have enjoyed my time at Bradford and should like to thank all concerned, especially the performance staff and players for their support."
Mark Dunning, who was Kear's assistant, has been appointed interim-coach and will be in charge for Sunday's game at Whitehaven.