Vauxhall MP Kate Hoey had complained to the Charity Commission about the project, citing concerns about spending by the Garden Bridge trust. Earlier this year, the trustees admitted the project could cost more than the £185m planned.
The commission found that "the trustees were meeting their duties and were acting in compliance with charity law", and the trust welcomed this outcome.
"We welcome the fact that the Charity Commission has endorsed our approach and we are always looking to learn lessons and make improvements," said Lord Mervyn Davies, chairman of the Garden Bridge Trust.
"The Garden Bridge is an inspirational project that involves the best of British design and innovation. It will be a landmark for central London and bring huge benefits to the capital and the UK. We now intend to draw a line in the sand about historical aspects of this project delivered by other parties and get on to make the Garden Bridge a reality."
However, Labour London Assembly member Tom Copley said the regulator's findings were not a line in the sand.
"This investigation deals only with claims about the Trust's financial irregularities," he continued.
"With Dame Margaret Hodge's review yet to report, we still don't have answers to questions about whether value for taxpayer money has been achieved. We already know from TfL's internal and external auditors that the procurement process for the bridge lacked openness and transparency.
"This is very much a live issue, with the future of the Garden Bridge continuing to hang in the balance. Even the Garden Bridge Trust aren't certain that the project is a going concern."
Copley added: "We need assurances that more public cash won't be squandered on a bridge that may never be completed. As we've made clear, our only chance of safeguarding against that is for the Mayor to refuse to put pen to paper on the maintenance guarantee."