Jeremy Richardson 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 at around 6.30am on Wednesday.
He was taken to hospital in a critical condition but died the next day, leaving a wife and three children.
The academy trust which runs the school, which he joined in 2016, has already issued a lengthy tribute to the much-loved senior leader.
He originally taught maths before taking on leadership roles at Sheffield Springs Academy and then Bishop Young C of E Academy in east Leeds.
West Yorkshire Police said: "Officers were called to reports of a vehicle in collision with a cyclist in Byron Street at 6.38am on Wednesday.
"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.
"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 22 June."