Scotland Yard launched the probe following revelations in the Sunday Mirror newspaper.
The Met said in September it would “assess” whether any criminal offences were committed by Vaz following the allegations of drug use and hiring escorts. It then launched an investigation last month.
Today, the Met said:
Following allegations in the Sunday Mirror on Sunday 4 September concerning a Member of Parliament, the Metropolitan Police Service received a letter on Wednesday 7 September requesting police consider the matter.
The letter was forwarded to the Special Enquiry Team, part of Specialist Crime and Operations, who started an assessment process to identify what criminal offences - if any - may have been committed. Following that assessment, which included obtaining early investigative advice from the Crown Prosecution Service, the MPS started an investigation in November.
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.
Vaz resigned as chair of the home affairs select committee, which he had headed up since 2007, following the claims.
"It is in the best interest of the home affairs Select committee that its important work can be conducted without any distractions whatsoever," Vaz said in a statement at the time.
"I am genuinely sorry that recent events make it impossible for this to happen if I remain chair. I have always been passionate about select committees, having served as either chair or member for half of my time in parliament.
"The integrity of the select committee system matters to me. Those who hold others to account, must themselves be accountable."