The star, known for roles in films as diverse as the animated hit Who Framed Roger Rabbit and the classic London gangland thriller The Long Good Friday, died from pneumonia on Tuesday.
Dame Helen Mirren said Hoskins was her big-screen "brother." She appeared alongside him in the gangland thriller and in Last Orders. The actress said: "Bob was a great actor and an even greater man. Funny, loyal, instinctive, hard-working, with that inimitable energy that seemed like a spectacular firework rocket just as it takes off.
"When I worked with him on his iconic film The Long Good Friday, he was supportive and unegotistic. He was never sexist, when many around at that time were."
She said Last Orders was like "playing a duet with a brother I had grown up with, which professionally I had. I personally will miss him very much."
Hoskins' portrayal of doomed career criminal Harold Shand in The Long Good Friday made him a film star and he followed it with stand-out roles in Mona Lisa and The Cotton Club.
His role as a petty criminal in Mona Lisa won him an Oscar nomination for leading actor. He also appeared in Who Framed Roger Rabbit and opposite Cher in Mermaids.
Scottish Line Of Duty actor Martin Compston, who acted with Hoskins in the post-apocalyse film Doomsday, tweeted: "Long Good Friday to Roger Rabbit Bob Hoskins a true legend had wee part in a film with him years ago and he was an absolute gentleman."
Samuel L Jackson said: "Truly saddened by the passing of Bob Hoskins! A truly Gigantic talent & a Gentleman."
Culture Minister Ed Vaizey paid tribute, saying: "Bob Hoskins has entertained audiences of all age groups around the world."
His wife, Linda, and children, Alex, Sarah, Rosa and Jack, said they were devastated by the loss of their "beloved Bob".