According to reports in The Sunday Times, Richard Sharp was involved in arranging a guarantor on a loan of up to £800,000 for Mr Johnson.
Mr Sharp said he had "simply connected" people and there was no conflict of interest.
Mr Johnson's spokesman said he did not receive financial advice from Mr Sharp.
James Cleverly has said that, as far as he can see, Richard Sharp’s appointment as BBC chair was made on his merits.
Asked whether the reports that Mr Sharp helped Conservative former prime minister Boris Johnson arrange a guarantee on a loan of up to £800,000 weeks before he was recommended for the job, the Foreign Secretary told Sky News’ Sophy Ridge On Sunday programme: “Well, I’ve not had a conversation with either of those parties about that, about that situation.
“I have met with Richard, we discussed the (BBC) World Service, he struck me as an incredibly competent, experienced, thoughtful individual. I can see exactly why he has the attributes, both personal, professional, to be the chair of the BBC.
“So, as far as I can see, his appointment was made on those merits.”
He added: “The fact of the matter is that Richard is undoubtedly an incredibly experienced individual, steps into this role with, as I say, both personal, professional attributes, which qualify him for the job.
“We’ve had senior people in the BBC who have political affiliations, most people have political affiliations, a number of them are active, so it’s not at all unusual to have individuals in the senior levels of the BBC.”
Reports that the BBC chairman helped Boris Johnson arrange a guarantee on a loan of up to £800,000 weeks before he was recommended for the job by the then-prime minister are “really corrosive to governance and government”, Labour has said.
Shadow Treasury minister Pat McFadden told Sky News’ Sophy Ridge On Sunday programme: “I feel more than the individual cases, this is really corrosive to governance and government, there are big problems facing the country.
“We need good government. I think it’d be a tragedy if the result of all this was for people to just simply turn away from politics and say, ‘they’re all a bunch of crooks and thieves’.”
Asked whether he thinks the BBC is impartial, Mr McFadden said: “Look, I’m not here to report for the BBC. I do think it’s pretty extraordinary if someone who is running to be the chairman ends up acting as a broker to help the prime minister of the day of whatever financial difficulties he was in.
“At the very least, that should all have been declared and brought into the open. There’s nothing in Boris Johnson’s declaration of interest as an MP about this. It’s been brought into the open by journalism, not by people being transparent, and that’s why I do think this does need to be looked at.”