“The loveliest light on Baker Street has gone out,” wrote Moffat of the late actor, who starred in the BBC series as Mrs Hudson.
“What a woman, what a talent, what a star - and just about the kindest, nicest, funniest person you could meet.”
Moffat, who co-created the show with actor and writer Mark Gatiss, remembered Stubbs as “the irreplaceable heart and soul of Sherlock”.
Gatiss also paid tribute to Stubbs in a post on Twitter: “It was one of the great joys of my life to work so closely with and to adore Una Stubbs. She was a wonderful, wonderful woman and a great and serenely graceful actor.”
“Mischief was in her blood,” added Gatiss. “We were so blessed that she became our imperishable Mrs Hudson. Goodbye, darling.”
Sherlock producer Sue Vertue and her team on the show wrote in a statement: “Oh Una Stubbs, how we will miss you. You famously said to Sherlock that you were ‘his landlady, not his housekeeper’ but to us, you were so much more than either of those things - you were absolutely our Sherlock mum.”
Vertue added: “You knitted us together. Always loving life, always wise, always wickedly funny and always kind. Bye bye you darling lady, you will always be in our hearts.”
The writer and broadcaster Gyles Brandreth wrote onTwitter: “Oh, this is so sad. Such a funny, lovely, gifted lady - a marvellous actress with a special style & a great (and impish) sense of humour. I first met her when she was in Cowardy Custard in 1972 & last saw her at Nicky Henson’s funeral last year. A sad day.”
The baroness Baroness Floella Benjamin wrote on Twitter: “Una Stubbs was not only a great actress but a delightful person, too. I remember appearing on her team in Give Us a Clue and she made my mum, who I took to the recording, feel very special. I’ll be eternally grateful to her for that. May she rest in peace.”
You can read more tributes to Stubbs here.
Additional reporting by Press Association