One of Walker's most famous lines was, "I've got to stop now, because I've got a lump in my throat" as Britain's Hill won the 1996 Japanese Grand Prix - and with it his only World Championship.
Hill added: "Maybe old soldiers never die? His legacy and his memory is so strong, and what he gave to so many Formula 1 fans and number of people he affected, he became bigger than the sport, so we have got a lot to be thankful to Murray for.
"He could emote the events that happened in our sport. The shocking moments and the dramatic moments all have Murray's reaction to them and he made those events stick in your mind forever.
"And he allowed himself not to be the know-it-all commentator, but the fan who, at times, got over excited."
Walker, who is survived by his wife of more than 60 years Elizabeth, was appointed an OBE in 1996 for his services to broadcasting and motor racing.
His co-commentators included the late James Hunt, who was F1 world champion in 1976, and the pair built up a memorable partnership.
He also had a popular partnership with former grand prix driver Martin Brundle, who paid tribute on social media.
"Wonderful man in every respect," said Brundle. "National treasure, communication genius, Formula 1 legend."
Three-time world champion Sir Jackie Stewart said he spent a lot of time with Walker, who served in a tank regiment during World War Two, as their fathers both knew each other.
"He was a very special man in every respect," the Scot told BBC Radio 5 Live. "I was lucky enough to know him well. In fact, I spoke to him several weeks ago where he was in a home.
"He was the perfect gentleman, a man who had great style and great skills with the English language.
"As a racing driver, from my own point of view, Murray was always the best."
Stewart added: "He was very good at making mistakes. He made wonderful mistakes. He so much enjoyed the realisation of his error, he was such a character.
"A mistake didn't mean anything wrong for Murray. It was something else to make a joke of.
"He was full of energy, he never sat to do a commentary. He stood up for the whole time."
Reigning world champion Lewis Hamilton also paid tribute, saying: "So sad to hear of Murray's passing. I remember growing up hearing your voice over the races. You made the sport so much more exciting and captivating.
"The iconic voice of our sport and a great man, thank you for all you did, you will never be forgotten. Rest in peace."
An F1 statement said: "We are immensely sad to hear that Murray Walker has passed away.
"His passion and love of the sport inspired millions of fans around the world. He will forever be a part of our history, and will be dearly missed."
Reigning world champion constructor Mercedes echoed the view that Walker was "the voice of F1 to millions" and added that "his love, passion and positivity for our sport were unmatched".
McLaren said: "He brought our sport to generations by sharing his passion and knowledge with humour and humility. Our thoughts are with all who had the fortune to know him."
James Allen succeeded Walker in the commentary box at ITV and told BBC Radio 5 Live: "He was so just much fun.
"The age difference between us was 45 years or something but he was so young in his mind.
"His career was in advertising, he was always aware of the audience.
"He was such a laugh. He didn't like driving much on the continent so, at all the foreign grands prix, I drove him around everywhere.
"One of my favourite stories, I drove him to a restaurant and when we came out there was a bunch of kids outside and one of them said 'that's Murray Walker's driver'.
"He had a life incredibly well lived."