He was 88.
The former political editor of Press Association, who was hailed as "the one journalist who mattered" by former Prime Minister Tony Blair, died in hospital on Friday morning after a short illness, his family said.
He retired after 32 years at Westminster in 1994, but returned to work the next day and continued to contribute to the agency until his death.
Pete Clifton, PA's editor-in-chief, said: "Moncrieff was the ultimate news agency journalist - great contacts, always close to the action, working some epic hours and obsessed by getting stories out before everyone else.
"He had no interest in any political agenda or viewpoint, just making sure he was first to write about it.
"On the rare occasion he took a holiday, we could expect him to file news stories he'd picked up on the promenade, and until very recently he was still filing us the 'quotes of the day' feature for the newswire, as well as drawing on his extraordinary memory to file a weekly politics column for our regional newspaper subscribers.
"Legend gets overused, but there's no doubt Moncrieff was a legend and a remarkable political reporter.
"We are profoundly sad today, but cheered by the many stories of Moncrieff we can share."
The Lancashire Post ran a column by Moncrieff for more than a decade.
Described in Westminster as "the man with the lived-in face and slept-in suit", Moncrieff's style was classic news reporting and he roamed Westminster with order papers stuffed under his arm and notebooks in his pockets as he encouraged MPs to call him at any time of day or night.
He joined the national news agency's parliamentary staff in 1962 before becoming a lobby reporter in 1973 and chief political correspondent (later political editor) in 1980.
Westminster's The House magazine said he was a "one-man dynamo for whom news is food and drink is Guinness".
The press bar of the House of Commons was named after him in 2007.
He had four children with his late wife Margaret.
Former prime ministers John Major and Margaret Thatcher were among those to praise Chris Moncrieff for his eye for a story but also as a remarkable character when he officially retired in 1994.
Tributes made upon his retirement
Paddy Ashdown said: "It is Chris Moncrieff's professionalism which so impresses. He seems never to take a holiday, but always to be on the end of a phone, and always cheerful.
But being the unassuming person he is, always presumes that nobody knows who he is.
"I have never known him refer to me by my Christian name or open a conversation even at some peculiar hour of the night with words other than: "Hello, my name is Chris Moncrieff, sorry to disturb you...", as though anybody who has been in politics for more than five minutes doesn't know who he is and anybody who has been in politics more than a year wouldn't recognise his voice at the first syllable."
Sir John Major
"Whenever I look up there you shall be and whenever you look up there I shall be." Chris Moncrieff is no Bathsheba but he has been ever present in the lives of many politicians, including me, I am glad to say.
Michael Brunson said: "Chris is a living reproof to any journalist who does not have shorthand, like myself.
"I confidently expect to see him, pad and pen poised, at the Day of Judgment, taking down every last word, because he seems to have recorded most of those spoken in and around Westminster for as long as most of us can remember.
Lord Mason of Barnsley: "You are a good man," was his constant reply to a bit of copy. I have never known in journalism a better 'good man'.
Michael Heseltine said: "No matter how outrageous the story you gave him, no matter how questionable the evidence behind the assertions you made, Chris Moncrieff was the enthusiastic recipient of your every phrase.
"Great!" he would comment, "Great! Any more?"
"He was a stimulus to us all. Not so much a tonic in the political process, the very bottle itself!
Sir Bernard Ingham said: "He has exercised great power and influence, as I can personally testify. What he writes appears in print, often untouched by other human mind, in countless newspapers up and down the country.
"His writ runs. His richly comic weekly summaries of the political scene delight millions.
"We are fortunate that Chris has taken his job - if not himself - very seriously. His application to the task of newsgathering is unparalleled. His eye for a story unerring, his professionalism and speed unequalled.
John MacGregor said: "The bloodhound of the lobby. There is never a sniff of a political story that Chris's nose has not followed up.
Neil Kinnock: "I never had to ask "Chris who?". No-one else would call at 9.30 on Saturday night or - on issues of exceptional excitement - 8.00 on Sunday morning.
"No-one else would take copy so rapidly, use it so avidly or spread it so widely.
"No-one else could make the unrehearsed opinions of a junior backbencher sound like the fount of wisdom.
"Or, come to think of it, unwisdom.
"There is a gargoyle - or it might be the weather-worn statue of a long dead king - in a niche overlooking Palace Yard that will forever be the graven image of Moncrieff.
Lord Callaghan of Cardiff said: "I well recall his early appearance at Westminster, and it seems as though he has never changed. He has always been himself; courteous, self-effacing, rumpled but unruffled.
"Whatever his personal views of the value of the stories we tried to interest him in, he has never failed to report them accurately, faithfully and without embellishment.
Tony Benn said: "I have three special memories of Chris. He was always available day and night and happy to receive news.
"When he himself telephoned he was always so modest - 'Moncrieff here' - as if I had never heard of him.
"He was both professional and courteous at all times.
Lord Parkinson said: "He has a great gift for making friendships, a nose for a good story and a wonderfully polite but persistent way of getting to the heart of the story.
"He must be a prime candidate for the Guinness Book of Records as the person who has filed more column inches in our newspapers than any other political journalist.
"His victims are approached with charm."
Baroness Thatcher said: "You have been superb in every way, honourable, thoughtful, fair-minded and good copy.
Geoffrey Dickens said: "As a detective or journalistic sleuth, Chris Moncrieff has no equal. His skill at hunting down the Member of Parliament he wishes to speak to is legendary. Let me give you an example.
"During recess I was staying with some dear friends in Salcombe, Devon. Chris Moncrieff's telephone call broke the silence of a lovely summer evening as we sat on the balcony overlooking the sea while enjoying a cool gin and tonic. "How on earth did you know I would be here, Chris?"
"Quite simple really. I recalled that on this week, four years ago, you went to your friends in Devon, so I kept the number to hand for future reference!"
Don't you think this is quite remarkable - I sometimes have a job to lay my hands on that number myself!