59-year-old Vaz, a Labour MP, had resigned as chair of parliament's influential Home Affairs Select Committee in September amid a sex scandal over allegations involving male prostitutes.
The Metropolitan Police had opened an investigation under the Misuse of Drugs Act 1971 last month.
"Following that assessment, which included obtaining early investigative advice from the Crown Prosecution Service (CPS), the MPS (Metropolitan Police Service) started an investigation in November," a Met Police statement said.
"During the investigation, new information was received and additional advice obtained from the CPS, following which the MPS has made the decision to close the investigation with no person being charged," it said.
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He was also accused of encouraging others to use poppers, an illegal party drug.
The Met had received a letter soon after the media allegations, calling for a police investigation.
The correspondence was passed on to a specialist team, which "started an assessment process to identify what criminal offences, if any, may have been committed".
A spokesperson for Vaz said, "The Metropolitan Police Service has informed us that they have decided 'not to proceed any further' with their investigation arising from reports in the Sunday Mirror and The Mirror and that the investigation is now closed".
The House of Commons watchdog - Parliamentary Commissioner for Standards - has also launched an inquiry into Vaz, who has since joined the Parliament's Justice Select Committee in October.