Last week it ruled Mr Fedorcio should face a hearing for gross misconduct.
But the IPCC said his resignation meant this could not now take place.
Report to follow The IPCC said it planned to publish the findings of its report into the relationship between Mr Fedorcio and Mr Wallis "in the next few days".
It was revelations about a former senior News of the World journalist having such a role at Scotland Yard which prompted the force's then commissioner Sir Paul Stephenson to resign in July last year.
Mr Fedorcio had been on extended leave since August pending the investigation into his relationship with Mr Wallis, who was arrested on suspicion of phone hacking last year but has not been charged.
Mr Wallis's company, Chamy Media, was paid £24,000 by the Met for PR advice between October 2009 and September 2010.
Mr Fedorcio told the Leveson Inquiry earlier this month Mr Wallis was hired as a consultant because "he wanted someone he knew and trusted".
He said he had taken the decision to take on a consultant in 2009 while his deputy was on long-term sick leave.
IPCC deputy chairman Deborah Glass said: "I have today been notified that Dick Fedorcio, the Metropolitan Police Service director of public affairs, has resigned."
She said that in July 2011 the IPCC decided to investigate "the relationship between Mr Fedorcio and Neil Wallis, a former deputy editor at the News of the World, focusing on the circumstances under which a contract for senior level media advice and support was awarded to Mr Wallis' company, Chamy Media."
That investigation ended late last year and a report was handed to the Met's professional standards unit on 10 January.
Ms Glass said: "Our investigation found that Mr Fedorcio has a case to answer in relation to his procurement of the contract for Chamy Media. Last week the Metropolitan Police Service proposed to initiate proceedings for gross misconduct and I agreed with that proposal."
But Mr Fedorcio's resignation means he cannot now face internal disciplinary proceedings.
Ms Glass said: "In light of Mr Fedorcio's resignation today, those proceedings cannot now take place and I propose to publish our investigation report detailing our findings, in the next few days."
Moving on The BBC's home affairs correspondent Tom Symonds said it was not yet clear if Mr Fedorcio had been offered some sort of severance package but he said it was a sign that Scotland Yard wanted to move on from the hacking scandal.
Mr Fedorcio told the Leveson Inquiry he had put the PR contract out to tender, asked two other firms to bid but ended up hiring Mr Wallis' firm.
He told Lord Leveson the bids from rival PR firms Bell Pottinger and Hanover were 50% more expensive than Chamy Media but he denied he knew that would be the case from the outset.
The Met confirmed Mr Fedorcio would be leaving his post as director of public affairs on 31 March after 14 years in the job.
"During that period he has made a very significant contribution to the work of the MPS," they said.
In July last year, MPs on the home affairs committee criticised Mr Fedorcio for failing to conduct proper checks on Mr Wallis before hiring him.
Mr Fedorcio told the Leveson Inquiry he asked Assistant Commissioner John Yates, who had conducted the initial phone hacking inquiry, what he thought about hiring Mr Wallis.
He told Lord Leveson he wanted to know of any potential risks to the organisation if Mr Wallis was engaged by the MPS in view of the phone hacking case.
Asked by the inquiry whether he would have taken on Mr Wallis if he knew he and Mr Yates were such close friends, he said he might have thought the hiring "inappropriate".
Mr Yates has told the inquiry he was "good friends" with Mr Wallis - they had had dinners together and attended a football match together.