The Prime Minister, who consulted his ethics adviser over the case, did not order a formal investigation and said his decision is “these matters do not amount to a breach of the ministerial code”.
Mrs Braverman had been accused of breaching the code by asking taxpayer-funded civil servants to help after she was caught speeding, with opposition parties demanding an investigation.
In his letter, Mr Sunak told the home secretary: "As you have recognised, a better course of action could have been taken to avoid giving rise to the perception of impropriety. I am reassured you take these matters seriously. You have provided a thorough account, apologised and expressed regret.
“It is vital that all those in Government maintain the high standards the public rightly expects.”
Replying, the home secretary said: “I sought to explore whether bespoke arrangements were possible, given my personal circumstances as a security-protected minister. I recognise how some people have construed this as me seeking to avoid sanction – at no point was that the intention or outcome.
“Nonetheless, given the fundamental importance of integrity in public life, I deeply regret that my actions may have given rise to that perception, and I apologise for the distraction this has caused.
"I regret that my attempt to find a way to participate in the course in a manner that would have satisfied these concerns has enabled some to construe a potential conflict of interest. With hindsight, I acknowledge that the better course of action would have been to take the points and fine upfront.”
She later accepted a fine and penalty points on her driving licence for the speeding offence. The Liberal Democrats criticised the lack of action, labelling it a “cop-out”.
Chief Whip Wendy Chamberlain MP said: "This is a cowardly cop-out from Rishi Sunak. With every scandal, we see the Prime Minister dither, delay and flip-flop, never taking decisive action. This is not the leadership the country needs during such a severe cost-of-living crisis. Sunak is too weak to even order an investigation, let alone sack his home secretary.
"Sunak had the chance to do the right thing, but instead he's once again chosen to be ruled by his own hardline backbenchers. He may be in office, but he is barely in power."