Leonard - who wrote more than 40 novels - died after suffering complications from a stroke yesterday morning. He was 87.
Ian Rankin was quick to heap praise on Leonard and said he was "a great writer".
The author said on Twitter: "Gave me a few tips once. I ignored most of them."
Many of Leonard's novels - including Out of Sight, Get Shorty and Be Cool - were made into films.
But he did not have a best-seller until his 60th year and few critics took him seriously before the 1990s.
He enjoyed some minor success in the 1950s and 1960s writing Western stories and novels, a couple of which were made into movies.
But his first crime novel, The Big Bounce, was rejected 84 times before it was finally published as a paperback in 1969.
Leonard followed up with several more well-written, fast-paced crime novels, including Swag in 1976.
Leonard married three times and had five children, all from his first marriage.