The Enric Miralles-designed project is now set to cost £240m.
The increase had been expected for some time as the budget was based on 1998 prices and left no room for inflation. It is also believed that some contracts are forecast to overrun.
A statement issued this week by the Scottish parliament said Ezzi was departing because "mutual expectations have not been fully realised". The statement added: "The pressures on this post are considerable and increasing."
Ezzi will be replaced by Sarah Davidson, a senior parliamentary staff member who has been working on the Holyrood project for more than a year.
Ezzi was previously capital projects director at Lothian University Hospitals NHS Trust, where he was responsible for the Royal Infirmary building in Edinburgh.
The project team includes contractor Bovis Lend Lease and QS Davis Langdon & Everest.