If Parliament agrees to the creation of a single watchdog under the ASA umbrella, it will be Graham, 53, a one-time BBC producer, who will lead it.
The new set-up, being introduced by Ofcom, will sweep away the current fragmented system and put all regulation, whether of broadcast or print material, internet ads and text messaging, under Graham's organisation.
The system includes the establishment of an Advertising Advisory Committee. This will sit under an independent chairman to provide expert advice to the broadcast rule-making body, the Broadcast Committee of Advertising Practice.
Ofcom will retain backstop powers including the option of re-imposing direct statutory controls if necessary, and the right to amend broadcast advertising codes in exceptional circumstances.
Ofcom's confirmation that it will contract out broadcast regulation to the ASA comes as the ad industry faces intense scrutiny over the issue of advertising to children.
However, Ofcom this week declared itself "satisfied that the proposed structure of the new system to be run un-der the ASA will create an effective, adequately funded and sufficiently independent co-regulator".
The system will be paid for by extending the existing 0.1 per cent levy on all non-broadcast advertising to broadcast ads.
If approved by MPs, the new levy will be in operation by the summer, just before the new system comes into being.
Ofcom's decision has been welcomed by industry bodies. Hamish Pringle, the IPA director-general, described it as "far-sighted" and added: "It takes into account consumer needs, media convergence and rapid social change, all of which require a faster, more flexible and more sensitive response than legislation can possibly provide."
Malcolm Earnshaw, his ISBA counterpart, said: "While drafting and communications systems for broadcast and non-broadcast will remain formally separate, the bringing together of all forms of advertising under the single ASA banner will lead to more joined-up thinking on both."
Andrew Brown, the Advertising Association's director- general, claimed the new system would sustain public trust in advertising by providing a single clearing house that would make it easier for people to lodge complaints.