Price was next in line to face Fury following his recent first round demolition of John McDermott, but the 23-year-old has decided to pursue a world title shot rather than battle his domestic rival.
Sexton has now been handed a shot against Price for the vacant belts and the Norwich fighter will hope to seize his second bid for the British title after falling short against Dereck Chisora in 2010.
He has previously held the Commonwealth title and Sexton, with a record of 15 wins and only two defeats, should prove Price's sternest test to date.
Simon Block, the Commonwealth Boxing Council honorary secretary, said: "The British Boxing Board of Control determined that Price box Sam Sexton for their national title, also vacated by Fury, and Sexton is a named challenger on the list of contenders issued by the CBC on 8th December.
"This match, subject to compliance with CBC Regulations, will also be recognized as being for our title."