Tamm - who played Romana opposite Baker's Fourth Doctor in 1978 and 1979 - recently passed away following an 18-month battle with cancer.
"The dreadful news of Mary Tamm's death amazed me," Baker wrote on his official website. "I had no idea she was ill. We got on terribly well and I admired her wit and style and warmth.
"We used to meet at different Who conventions and sometimes had time for a little chat. I remember meeting her at Heathrow in the first class section: her section, of course. She was flicking through a magazine and sipping a beer: the epitome of cool style."
78-year-old Baker also reflected sadly on the passing of fellow Doctor Who companions Elisabeth Sladen (Sarah Jane Smith) and Caroline John (Liz Shaw).
"Fate is capricious and quite indifferent to our fears," he wrote. "Lovely girls: Elisabeth Sladen, Caroline John and now Mary Tamm: all dead. And here am I closing in on 80 and all I've had was whooping cough! It's not fair, is it?"
He concluded: "I never met Mary's daughter and hardly ever met Marcus, her husband. But I send them from the bottom of my old heart sincere condolences. To have known her consoles me a little: poor darling Mary, poor us."
> Doctor Who star Mary Tamm 1950-2012: Her career in pictures
Watch a clip of Tom Baker and Mary Tamm in Doctor Who below: