"It's important we get to the bottom of what went wrong so that we are better prepared for future disasters," Woods said.
"We also need to look at what was done well, and what has worked better in the Kaikoura earthquake sequence."
The inquiry will have powers to compel evidence, hold public hearings and would inform amendments to the Earthquake Commission Act.
The main Budget initiative for Christchurch has already been announced - $300m over the next year to accelerate rebuild projects in the city.
It is up to the Christchurch City Council to decide how the money will be spent on the various projects, which include a roofed, multi-purpose stadium.
"The fund is being guided by what the people of Christchurch want," Woods said.
"While all the projects will of course need satisfactory business cases, we are not making Canterbury decisions from Wellington."