The Scottish stand-up features in a one-off comedy with Bob Mortimer that will run exclusively on the on-demand service which is not covered by Ofcom's broadcasting code.
Hundreds of people complained to the watchdog which ruled that Channel 4 breached broadcasting guidelines after Boyle made comments about Katie Price's disabled son on his series Tramadol Nights in 2010.
The BBC's head of TV Mr Cohen said: "The Ofcom guidelines are very important, but we also have our own editorial standards and values that we keep to across everything we make, and we will be making sure Frankie adheres to those.
"We don't have a ban on any particular comedian and nor should we.
"I imagine you're talking partly about the stuff on Channel 4, which was not a joke I liked but at the same time we're not in the business of banning specific comedians because of jokes they may have told."