Harry and Meghan’s spokesman criticised the “baselessness of the claims” and said the review underlines “the legitimacy of the former charity”.
Republic, which campaigns for an elected head of state, reported the foundations of the Sussexes and the Duke and Duchess of Cambridge to the regulator in July last year.
The claims were made after the Sussex Royal charitable body, which later became known as MWX Foundation before being wound up, received a £145,000 start-up grant from William and Kate’s Royal Foundation.
A further sum of £151,855 was transferred from the Royal Foundation to MWX to deliver Harry’s Travalyst sustainable travel programme, and was later transferred by MWX to the Travalyst organisation.
But the Commission found that all transfers of funds were lawful.
A spokesman for Harry and Meghan said: “We are pleased that the Charity Commission has confirmed what we knew from the start: that MWX Foundation, formerly Sussex Royal, complied fully with UK charity law in its handling and transferring of funds and grants.
“Today’s update provides complete closure to this review and ultimately underscores both the legitimacy of the former charity and the baselessness of the claims against it.”
The Republic pressure group issued a lengthy apology to the charities and to Harry on its website.
It admitted that it “falsely claimed” that the transfer of funds was improper and likely to be unlawful.
It said: “We apologise unreservedly to the charities and personally to the Duke of Sussex for our actions and the public damage that has been caused as a result of widely publicised untrue claims.”
The Charity Commission found that the transfer of funds to MWX – which was formerly Sussex Royal: The Foundation – was in line with the governing document of the Royal Foundation and allowed under charity law.
It also found that the transfer of funds by MWX to not-for-profit sustainable travel organisation Travalyst was lawful.
The Commission further found that Travalyst could receive charitable funds for the promotion of sustainable travel only, which is a charitable activity in law, and there was no evidence to suggest that any conflicts of interest between MWX and Travalyst were managed inappropriately.