The company was preparing to announce the appointment in the New Year, but it has chosen to finalise the decision before Christmas.
Current chief executive Ralph Bernard confirmed in November that he had decided to retire and would step down as soon as a replacement had been found.
Hazlitt was one of three internal candidates, together with operations director Steve Orchard and financial director Wendy Pallott, while external candidates included ex-Chrysalis Radio chief executive Phil Riley.
A nominations committee was set up to make recommendations to the board, while headhunters Bird and Co were appointed to assist the search.
While Hazlitt is rumoured to be unpopular with The City, one senior member of GCap has said privately that he would leave the company if she was not given the job.
Bernard will continue at GCap as chairman of Classic FM, where he will oversee the station's licence renewal process, and will remain chairman of Digital One.