She was 46 and had been battling the disease for five years.
A statement from her agent said she died in hospital.
Siller played Revd Esther Warren on the ITV show, co-stars have spoken of their devastation.
She was a key part in the "who's the father" saga involving the Platt family and was also known for parts in Casualty and her role as Marilyn Dingle in Emmerdale.
Antony Cotton, who plays Sean Tully in Coronation Street, said: "Morag Siller. What a woman. She was a magnificent human being. Devastated."
Sally Dynevor, who plays Sally Metcalfe in the soap, said: "I feel very lucky to have met her but I am devastated that she has passed away, she was such an amazing, generous, kind woman and a fantastic actress - just a beautiful human being".
Lee Boardman, who portrayed Jez Quigley, tweeted: "So sad to hear of the passing of the wonderful Morag Siller. She played my girlfriend in Ladies Of Letters & was a delight. God bless you M."
A statement from AHA Talent Agency said: "It is with enormous sadness that we have to report the death of our beloved friend and client, Morag Siller.
"A brilliant, moving and funny actor whose credits are too numerous to name, we know she'll be remembered for her most recent stage appearances as Voltemand in Hamlet at the Barbican last year and as Puttana in Tis Pity She's A Whore at the Globe, as well as her performances in Les Miserables and Mamma Mia.
"Her many screen appearances included the ITV comedy series Ladies Of Letters and playing regular character Leona in Casualty.
"Morag will also be remembered for her extraordinary warmth, generosity and mischievous sense of humour as well as the fearless determination she displayed as she fought cancer whilst simultaneously raising tens of thousands of pounds for local charities.
"She was a truly inspirational person who we are incredibly proud to have represented. We will miss her hugely."