Ms Williams dedicated her win to her brother, Aaron, and thanked all her supporters.
"The task will be big and it will be tiring, but it will be worthwhile."
Ms Williams also paid tribute to those who have held the seat for Labour since 1922.
Labour Party Leader David Cunliffe congratulated his new MP on her "stonking good swing" to Labour.
"Parliament has just got an extraordinary new MP," he told a large and boisterous Labour Party celebration at Chisnallwood Intermediate.
He praised her for her dignity, grace, quiet determination, and "her love for her people, (which) just shines through."
Campaigning focussed on the issues that have plagued quake-stressed locals - housing, insurance, and EQC wrangling.
Three years on from the earthquakes, it was "time for a better deal for the people of Christchurch", Mr Cunliffe said.
The electorate, which was badly hit in the Canterbury earthquakes and seen voter numbers plummet by about 10,000 people.
Voter turnout had been seen as key for the by-election, and last night just 13,318 votes were counted, with 573 special votes.
A total of 3241 advance votes had been cast by the end of last night, according to the Electoral Commission, compared with 5229 at the same stage during the last general election.
But it was the highest number of advance votes cast for a by-election anywhere in the country.
