The capsules -- a broken glass bottle containing a handwritten note and a tightly-sealed metal cannister -- were found early today in Cathedral Square under the plinth of the statue of Mr Godley, known as the founder of Canterbury.
Christchurch Mayor Bob Parker said the "wonderful artifacts" would be preserved at the city's museum.
"We think that in these two things are contained the vision of our forbearers," he said.
"We think that when we open these we will gain an extra understanding of why they came here, what was their hope, what was their vision, what was their goal."
Mr Parker also said the statue would be repaired "with due regard to heritage".
"The first thing that we will do in this city is put back up on that plinth the man whose vision it was."
Two contractors who discovered the capsules, Sean Hegarty and Steve Proud, said what appeared to be a note fell from the glass bottle.
"We didn't dare touch it just in case it disintegrated," Mr Hegarty said.
"There was writing on it, very nice handwriting. You can't read it but there is writing on it."
The metal cannister was blank and sealed at both ends.
Mr Proud said the capsules would have to be carefully analysed by experts to prevent damage.