Mr Nemtsov, a leading critic of president Vladimir Putin and of the war in Ukraine, was gunned down near the Kremlin on the eve of a major rally in Moscow.
The Prime Minister said he was “shocked and sickened by the callous murder” of “a man of courage and conviction” who was “greatly admired in Britain” not least by former PM Margaret Thatcher.
“Boris Nemtsov is dead. But the values he stood for will never die,” he said in a statement.
Mr Putin is reported to have taken personal charge of the investigation which his spokesman said “has all the makings of a contract hit and is extremely provocative”.
Paying tribute to the murdered politician, Mr Cameron said: “His life was dedicated to speaking up tirelessly for the Russian people, to demanding their right to democracy and liberty under the rule of law, and to an end to corruption.
“He did so without fear, and never gave in to intimidation. He was greatly admired in Britain, not least by his friend Lady Thatcher, who visited him in Russia and who would have been appalled by today’s news.
“The courage of Nemtsov’s life contrasts with the utter cowardice of his murder.
“I extend my condolences to Boris Nemtsov’s family and friends. The Russian people have been deprived of a champion of their rights.”