Kirsty McCaskill said her father had been living with dementia for the past five years and passed away on Saturday.
She described him as a “lovely man” who brought “sunshine to people’s lives”.
McCaskill, who retired in 1998, was recognised for his Scottish accent and known during his career for his exuberance and enthusiasm for anticyclones, warm fronts and isobars.
He became the most imitated BBC TV weather forecaster during his 20 years presenting weather for the corporation and even had his own Spitting Image puppet.
In a statement on behalf of his family, Ms McCaskill said: “Ian was a truly lovely man who loved his family unconditionally and brought lots of sunshine to people’s lives with his friendly smile, kindness and sharp wit.
“He is survived by his wife Pat, whom he adored, two daughters, Vicky and Kirsty, two step-sons, Tim and Matthew, and nine grandchildren. He will be deeply missed.”
Liz Howell, head of BBC weather, said McCaskill was “one of the most popular BBC weather presenters”.
She added: “He served the British public and the corporation with distinction for 20 years. Our sincerest condolences go out to his family at this time.”
The Met Office said he was a “much loved colleague and will be sadly missed”.
BBC weather presenter Carol Kirkwood, who worked with McCaskill, said he was a “kind and very gentle man”.
“He was a funny man as well and exuberant, enthusiastic in his delivery and passion and love for the weather,” she said.
She said how he found his Spitting Image character “really funny” and he would laugh about it because “it was quite true to character in some ways”.
Former BBC weather presenter Peter Gibbs recalled how McCaskill had arrived at work late on a cold day as his car would not start.
Gibbs said: “He actually went on air and his introduction was ‘I now know what Vorsprung durch Technik means. It means your car won’t start’, with a real twinkle in his eye.
“Someone very high up from a well-known German car manufacturer was on the phone within minutes of him coming off air and the car was fixed very quickly.
“I don’t think we’d get away with that these days.
Former BBC weather forecaster Liam Dutton paid tribute to him on Twitter, saying: “Sad news about Ian McCaskill – a BBC weatherman I grew up watching. He was a lovely guy with a good sense of humour.”
Weather presenter Paul Hudson, who co-wrote the book Frozen In Time with McCaskill, wrote: “Really sorry to hear Ian McCaskill has passed away. We had great fun writing our book Frozen In Time. A warm, funny, generous and kind man.”
Impressionist and comedian Rory Bremner said he was a “lovely man” who was “pretty much part of the cast of our C4 show”. He added: “So many Geoff Atkinson sketches.”
McCaskill was born in Glasgow and educated at Queen’s Park School, Glasgow and Glasgow University, where he studied science.
National Service took him into the RAF and in 1959, he joined the Meteorological Corps as an airman meteorologist.
He left the RAF in 1961 to join the Met Office and was posted to Glasgow Prestwick Airport, Malta as well as the Manchester Weather Centre.
He transferred to the London Weather Centre in 1978 and became a member of the BBC’s forecasting team.
( From BBC website)