It was popularised by Sir Jimmy Young on his mid-day (I just typed 'mad-day' - freudian or what!) Radio Two Show from which he retired recently. Sir Jim went on to coin a whole array of phrases, which unfortunately, along with his increasingly singsong delivery meant that he sounded unlike anyone else you ever hear anywhere - although Terry Wogan is ploughing his own deep furrow on that score. I'm not criticising - just adding a bit of info.
It goes back way beyond Sir Jim's broadcasts. It was coined by Fred Kavanagh, scriptwriter to Tommy Handley, a star comedian on radio in WWII. His show was called ITMA for 'It's that man again'. Among many catch phrases TTFN 'Ta Ta for now' figured as the sign-off for some sketches and invariably as Handley's closing line to the show. The idea was amusing to servicemen in wartime; on joining up they found many odd acronyms used in the forces ;this mocked the use of them by officialdom