The actress died at home in London surrounded by her family.
The standup comic found fame with her TV series Victoria Wood As Seen On TV in the 1980s and she also stared alongside Julie Walters in Wood and Walters in the 1980s.
She also wrote and starred in popular TV series Dinnerladies.
In 2006, she won two Bafta awards for acting and writing for her drama Housewife, 49, an adaptation of the diaries of Nella Last.
In 1997, she was made an OBE in the Queen's Birthday Honours and was then made a CBE in 2008.
Her publicist, Neil Reading, said: "Victoria Wood has sadly passed away, after a short but brave battle with cancer.
"The multi Bafta award-winning writer, director, actor and comedian died peacefully at her north London home with family this morning. She was 62.
"The family ask for privacy at this very sad time."
Prime Minister David Cameron tweeted: "Victoria Wood was a national treasure loved by millions. My thoughts are with her family."
Wood's fellow comedians were also quick to pay their respects on social media, with Rory Bremner writing: "No. NO. This is too much. Now lovely, warm, funny, brilliantly talented Victoria Wood has gone. Words, songs, plays, she wrote the lot. So sad."
Jack Dee tweeted: "I feel privileged to have known and worked with the great Victoria Wood. Unique and truly brilliant," while Ricky Gervais wrote: "RIP the brilliant Victoria Wood. So innovative, funny and down to earth. This has not been a good year."
Journalist and author Caitlin Moran described the early influence Wood had on her, saying: "Seeing Victoria Wood on TV - working class, bookish, silly, clever, doing stand-up, singing, acting - made me think 'Girls can do this'."