The inciden occurred on the "Saturday Kitchen Live" programme on BBC1 that was broadcast on 5 December. Tom Kime apparently said "fucking hell" under his breath when he found omelette sticking to the frying pan.
Ofcom said the show breached rules prohibiting the broadcast of the most offensive language before 9pm.
BBC tendered an apology to the viewers and confirmed to Ofcom that the Kime would not return to the show.
Initially, the Corporation had refused to apologise, arguing that the programme's presentation and production team had not heard the chef's swearing.
Ofcom, however, cleared comedian Jimmy Carr of breaching broadcasting regulations when he referred to the pope as "king of paedophiles" on his Channel 4 quiz show 'Eight Out of 10 Cats' on 2 February.
The regulator also cleared ITV1's Alan Titchmarsh for featuring a package on sex toys in the run-up to Valentine's Day on 10 February.