Sophia Gardens will host an Ashes Test match between England and Australia in 2009.
"All the requirements that we laid down for awarding the fixture is very much on schedule," Morris added.
"The project meets our expectation and out satisfaction."
The £9.5m redevelopment will see capacity increased from 5,500 to 15,643.
The Cardiff venue gained the Ashes honour ahead of the established Old Trafford and Durham's Riverside stadium.