Catto will take up his post in December, replacing current Hyder chief executive Tim Wade, who is due to retire.
Announcing the appointment, Hyder Consulting chairman Sir Alan Thomas said: "Hyder has grown very successfully over the last nine years under Tim's leadership and we are pleased to have appointed someone of Ivor's calibre to take the company through the next phase of its development."
Under Catto's leadership, Atkins' Design and Engineering Solutions business has grown from 3,000 to 5,000 staff over the past three years and had revenues of £373.6M in the financial year to 31 March 2008.
Catto joined Atkins in 2000, and previously held roles in Scottish Power and Babtie Group.
"Hyder presents an exciting opportunity for me," said Catto.
"It is a natural extension of my prior responsibilities and I'm keen to begin pursuing the broad range of opportunities in front of the company. With the capabilities and skills currently in place within Hyder, it is well placed to continue to build upon the company's success and there is a great team to do this."