The former senior official is set to take over the role of chief of staff from Sir Keir Starmer in September.
She was approved for the post after a six-month deliberation by the Advisory Committee on Business Appointments (Acoba), the anti-corruption regulator.
But a separate Cabinet Office inquiry found that Ms Gray, who refused to testify in the Government inquiry, had breached the Civil Service Code for contacting Labor before she resigned in March.
Labor called the investigation “Mickey Mouse nonsense”.
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Cabinet Office Minister Jeremy Quin said: “I can now confirm that the Cabinet Office’s process of investigating the circumstances leading to Ms Gray’s resignation has been completed.”
“At the trial, Ms Gray was given an opportunity to speak but decided not to.
“This civil service-led process found that the order of service was breached on the face of the undeclared contact between Ms Gray and the opposition leader.”
“The rules and guidelines governing the conduct of officers are clear and transparent. It is deeply unfortunate that events have transpired in this way.”
Acoba on Friday recommended Ms Gray a six-month cooling off period from the day she left public service before taking up her new role with the opposition, allowing her to take office in two months.
The regulator concluded that there had been “no evidence” that her decision-making or impartiality had been “compromised” while serving at Whitehall.
Government officials had lobbied Acoba to introduce a 12-month waiting period after complaints about Ms Gray’s move to join the Labor leader after she opened a high-profile probe into Boris Johnson for lockdown violations in No. 10 had directed.
But while Acoba leader and Conservative colleague Lord Pickles said he “shared” some of the concerns expressed by departments about the potential threat to the integrity of the public service from their job change, he dismissed calls for a longer delay.
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In response to the Whitehall Inquiry’s conclusion, a Labor Party spokesman said: “All the rules have been observed. The Acoba process makes that clear.
“This statement is a political ploy by a Tory government out of ideas and out of control.
“It says everything you need to know about the Tories that they wasted weeks on this Mickey Mouse nonsense while refusing to investigate the serious allegations of sexual assault against their London mayoral candidate, Daniel Korski.
“We look forward to Sue Gray joining us this September as we continue to show the country that only Labor can build a better Britain.”
Mr Korski, a former Downing Street adviser during David Cameron’s tenure, last week withdrew from the race for the position of Tory candidate who could face Sadiq Khan in the capital after reportedly a decade ago a TV producer had been groped in #10.
The Cabinet Office has ruled out an investigation into Daisy Goodwin’s claims, which Mr Korski “categorically” denies.