Tamm's agent, Barry Langford, said the Bradford-born actor died at her home in Battersea after suffering from cancer for 18 months.
Tom Baker, who played the Time Lord to Tamm's Time Lady said: "She was a darling companion and wonderfully witty and kind. I'm so sorry to hear of her death."
His successor, Colin Baker, tweeted: "Shellshocked to hear Mary Tamm is gone. A funny, caring, talented, lovely and down to earth lady."
Her husband, Marcus Ringrose, said: "Mary was truly beautiful in every way. She was a very spiritual lady who loved nature and adored all animals. On set and offstage, her earthy northern humour and self-deprecating wit brightened every occasion. She was a consummate actress, and immensely popular in the profession."
Following her one-season stint on DOCTOR WHO Tamm appeared in BROOKSIDE in the mid-1990s, when she played snooty Penny Crosbie.
One of her earliest film roles was as Jon Voight's character's girlfriend in The Odessa File in 1973. Three years later Tamm starred as Terry's glamorous Finnish girlfriend in The Likely Lads film.
More recent roles have included parts in the TV series WIRE IN THE BLOOD and JONATHAN CREEK, and in 2009 she had a brief role as Orlenda in EASTENDERS. Throughout her career, Tamm's appearances included CORONATION STREET, THE BILL, HOLBY CITY and CASUALTY.
Langford, Tamm's agent of 22 years, described her as one of his closest friends, and said: "She had a great zest for life. She was a fantastic actress – she played stage parts of such range, parts that would take your breath away. She could play any role, and do so wonderfully."
Tamm leaves her husband, a daughter, Lauren, and grandson, Max.