Mr Hoggart, who spent the majority of his career at The Guardian, including a lengthy stint as its parliamentary sketch-writer, died yesterday after losing his battle against pancreatic cancer.
Mr Blair said: "It's a very sad moment for UK journalism. Simon was an outstanding commentator and writer with extraordinary wit, humour and insight. My deepest condolences and sympathy to all his family."
As well as his countless witty dispatches from Parliament and party conferences, Mr Hoggart was the author of dozens of books.
He was a regular broadcaster, chairing the News Quiz on BBC's Radio 4 for a decade.
Guardian editor Alan Rusbridger said he wrote with "mischief and a sometimes acid eye about the theatre of politics".
He said: "A daily reading of his sketch told you things about the workings of Westminster which no news story could ever convey. He will be much missed by readers and his colleagues."
Conservative MP Michael Fabricant, a regular target of Mr Hoggart's sketches, said: "Such sad news. He teased me mercilessly but always kindly."
Referring to his time at the helm of the News Quiz, his Radio 4 colleague Corrie Corfield said: "Like to think that somewhere rather special Simon Hoggart is now being told to get a move on by Alan Coren, with lovely Linda Smith laughing."
Mr Hoggart grew up in Hull and Leicester.