The crash happened in East Street, near Leeds city centre, at about 5.45pm on April 21.
Vincent Cullinane, 51, was riding a black Boardman pedal cycle when it crashed with a blue Carrera electronically-assisted pedal cycle.
He suffered serious injuries from which he never recovered. He died on Tuesday May 10.
The rider of the other bike, a 19-year-old man, suffered a minor leg injury.
The crash is now being investigated by the Major Collision Enquiry Team, who are keen to speak with anyone who witnessed it, or the moments leading up to it.
Anyone who can assist is asked to contact the team via 101, quoting log 1386 of April 21 or online via the LiveChat.