Police are appealing for witnesses following the incident.
Jeremy Richardson, 61, was cycling from his home in Leeds to Beckfoot Thornton School in Bradford when he was hit by a vehicle on Byron Street in Barkerend.
West Yorkshire Police, confirmed in a statement:
"Officers were called to reports of a vehicle in collision with a cyclist on Byron Street at 6.38am on Wednesday morning (June 22).
The cyclist, a man aged 61 from Leeds, was taken to hospital with serious injuries. He has since passed away.
The driver of the vehicle stopped at the scene and is helping police with their enquiries."
Mr Richardson originally taught maths before taking on leadership roles at Sheffield Springs Academy and then Bishop Young C of E Academy in east Leeds.
A letter published on the school's website said:
"It is with immense sadness that we announce the passing of Mr Jeremy Richardson, the much-loved Headteacher and Executive Headteacher at Beckfoot Thornton and our Trust.
"Our whole school and Trust community has lost an incredible leader and a wonderful man, and his wife and three children a much-loved and devoted husband and father."
Officers would like to speak to anyone who witnessed the collision, or who has dash cam footage of the collision itself.
Anyone with information is asked to contact police via the LiveChat at www.westyorkshire.police.uk/contactus or 101 quoting log 245 of June 22.