Golunov, who maintained his innocence and claimed to be the victim of a set-up, was placed under house arrest on 8 June.
Mr Golunov, 36, is a freelance journalist who had been working for the Latvia-based news website Meduza, among others.
The reporter could have faced up to 20 years in prison if he had been tried and convicted.
Before the police backed down, almost 25,000 people had signed up to a Facebook page expressing their intention to take part in a protest march on Wednesday in solidarity with Golunov.
In Canada, Foreign Affairs Minister Chrystia Freeland told reporters, "We are following the current situation in Russian Federation very closely and with great interest and attention".
"This a very bad story", he said. "This is either unprofessionalism, recklessness or a provocation".
Fellow journalists and members of Russia's cultural elite suspect a set-up by corrupt officials wanting to silence him.
The Kremlin admitted on Monday that mistakes had possibly been made in the handling of the case.
Golunov disappeared on Thursday afternoon and turned up in police custody over 12 hours later. Badamshin said forensic tests had not detected the journalist's fingerprints on the bags of drugs purportedly seized from his home.
Police said they had found packets of mephedrone among his things, as well as cocaine and a set of scales in his apartment. They later retracted the statement, saying that the pictures were taken elsewhere. Human rights groups said police in Russian Federation often plant drugs on suspects.
The circumstances of Golunov's arrest have alarmed the media community. Presenters on Channel One, state media's flagship channel, also demanded a transparent investigation into the case.
All charges against Russian reporter Ivan Golunov have been dropped, after a huge public outcry.
The three leading daily newspapers - Vedomosti, Kommersant and RBK - all carried the same headline on Monday in a rare show of solidarity: "I am/We are Ivan Golunov".
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