The 59-year-old Labour MP for Leicester East recently quit as chairman of the Commons Home Affairs committee after the Sunday Mirror revealed he had paid for the services of two male escorts and allegedly offered to buy cocaine for their usage, not his own.
Police said they received a letter on 7 September asking them to look further into the matter.
The Metropolitan Police Service's (MPS) Special Enquiry Team began an assessment process to see “what criminal offences – if any – may have been committed”.
An MPS spokesman said: “Following that assessment, which included obtaining early investigative advice from the Crown Prosecution Service, the MPS is now investigating offences under the Misuse of Drugs Act 1971.
“The investigation started on Thursday, 10 November.”
The married father-of-two has welcomed the investigation, telling The Guardian: “I welcome a full investigation as a means of establishing the true facts and I am confident the police will pursue all lines of enquiry.
“I will cooperate with the investigation in any way I can.”
Before he stepped down from his role as chairman, the Home Affairs committee was involved in investigating prostitution and legal highs.
Mr Vaz joined the Commons justice committee in October despite the opposition of Conservative MP Andrew Bridgen.
Mr Bridgen told the Commons at the time: “I would leave the House with this question: If the right honourable member for Leicester East found himself last month to be not fit to be chair of the home affairs select committee and the matters are unresolved, what makes him think that he is a fit and proper person this month?”Reuse content