McCoist has accepted the apology, which was read out by BBC Radio Scotland as Rangers met Malmo in a Champions League match last night.
"I was adamant I would not speak to the BBC until the matter was resolved to my satisfaction so I am pleased an apology has been issued today,” The Guardian quotes McCoist as saying.
"I have always been generous with my time as the media play an important role in modern football but I will not tolerate being portrayed in the manner I was last week.
"Having worked in television for many years, with the BBC, I know exactly what was done last Friday and I was disgusted with their editing of the pre-Hearts press conference.”
Rangers kicked off their new campaign in the SPL with a home 1-1 draw against Hearts.