The move by Boaden and Steve Mitchell follows the announcement that BBC director general George Entwistle on Saturday had quit after just 53 days in the job.
The corporation has not yet confirmed the latest moves, but an announcement is expected within hours, reports BBC News.
The Guardian's Lisa O'Carroll says that head of newsgathering Fran Unsworth will take over as head of BBC News, and the editor of Radio 4's Today programme, Ceri Thomas, will take over as deputy.
Entwistle resigned after a Newsnight report led to a former Tory minister being wrongly accused of child abuse.
[Left: George Entwistle / Right: Lord Patten]
His short time in charge of the BBC was also dogged by controversy over alleged sexual abuse by former BBC presenter Jimmy Savile.
Before quitting, Entwistle commissioned two inquiries into the scandal, including one into the decision not to broadcast a Newsnight report on allegations that the Jim'll Fix It star was a paedophile.
Entwistle was director of BBC Vision when then report was dropped, and Boaden was the director of BBC News.
Tim Davie, the former head of BBC audio and music who is scheduled to take over at commercial arm BBC Worldwide, is acting director general following Entwistle's departure.
Lord Patten, the BBC chairman, says that the search is now on for the next BBC director general, who will be expected to right the ship and restore trust in the embattled corporation.
The former Tory MP is expected to speak again to the previous director general candidates - including the BBC's former chief operating officer Caroline Thomson and Ofcom chief executive Ed Richards - along with "one or two other names".
Lord Patten has said that an appointment could be announced "within weeks".