Ms Braverman resigned from Liz Truss’s Government after she sent an official document from her personal email to a fellow MP.
The Levelling Up Secretary told Sky News’s Sophy Ridge on Sunday programme: "Suella is a first-rate, front-rank politician.
"She acknowledged that a mistake had been made. She is working hard in order to ensure that our borders can be made more secure, and that policing is more effective.
"She’s a valued member of the Cabinet and someone whom I admire and like."
Later, Mr Gove told the BBC’s Laura Kuenssberg, is a politician of integrity after he was shown an email from Ms Braverman to her colleague.
He then added that he was satisfied that Ms Braverman should be brought back into the role after she resigned, apologised and took full responsibility.
In response, however, Shadow Home Secretary, Yvette Cooper demanded “proper answers” over the incident.
She told Sky News: “We have to have proper answers about whether or not this was the first security breach from Suella Braverman.
“We think that the papers and the warnings that were provided by the Cabinet Office and by the Cabinet Secretary to the Prime Minister should be sent to the Intelligence and Security Committee.
“So far, we’ve been asking repeatedly whether the Home Secretary has used her personal phone to send other Government documents.
“There’s also questions about whether she was investigated for other security leaks, including around a case involving security service, and around a case involving sensitive legal advice around Northern Ireland.
“Now, this is just irresponsible. You can’t have a Home Secretary who is not trusted by the security service, who is not trusted with important Government information.
“And it really shows the huge error of judgment that Rishi Sunak has made in reappointing someone just six days after she broke the ministerial code over security lapses, reappointing her to this immensely serious position.”