She died at the Christie hospital in Manchester on Thursday morning.
Oxberry became well-known nationally on Radio 1, working alongside Simon Mayo and Steve Wright, during the 1980s.
After studying meteorology, she joined BBC North West Tonight in 1994 as a weather presenter and fronted Inside Out North West's current affairs show.
BBC North West Tonight (NWT) presenters Roger Johnson and Annabel Tiffin said they were "heartbroken".
Former presenter Gordon Burns, who worked with Oxberry on NWT after leaving The Krypton Factor, posted a tribute on Twitter.
Totally, utterly, completely devastated. Just can’t believe we have lost the lovely hugely talented Dianne Oxberry. @BBCNWT will never be the same again. She was an outstanding broadcaster, brilliant colleague for so many years and a very good friend. Heartbroken.— Gordon Burns (@mrgordonburns) January 11, 2019
After her time at Radio 1 in London, Sunderland-born Oxberry returned north to Greater Manchester in 1993 with her husband, cameraman Ian Hindle.
The couple, who have two young children, met in Manchester while she was co-presenting the Saturday morning children's television show, The 8:15 From Manchester.
Mr Hindle said: "Dianne was an amazing wife and mother who embraced life to the full.
"She was an inspiration to all who knew and loved her but also to the people who watched and welcomed her into their homes each night as if she were part of their family too.
"She will leave a massive void in our lives but because of the remarkable person she was she will forever live on in our hearts.
"The children and I will miss her more than anyone can imagine."
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