The sponsorship, which takes in five leading US dramas and at least three UK dramas, kicks off on 7 June with a late-night series, Sugar Rush, written by journalist Julie Burchill. It will air on Channel 4 and E4.
Other dramas covered by the deal include Lost, an adventure series created by JJ Abrams, the man behind Alias. Lost follows 48 castaways after they crash onto a remote Pacific island.
The deal also takes in the second season of cosmetic surgery drama Nip/Tuck, the 11th season of ER, and season two of missing persons drama Without A Trace.
British shows include Ghost Squad, an eight-part series from Company Pictures that deals with moral issues surrounding policing the police force.
The Queen's Sister, meanwhile, is a drama about the late Princess Margaret, and stars Lucy Cohu in the lead role, with David Threlfall as Prince Phillip.
OMD Fuse negotiated the sponsorship, with media planning by Element.
The sponsorship idents were created by WCRS and directed by 4Creative.
The Number's marketing director, Alexandra Lewis, said the sponsorship opened up new creative opportunities for the 118 118 brand.
'We can present the original 118 twins in a new and appealing way,' she said. 'The Channel 4 drama audience is dead centre of our target market. (With this deal) we are driving awareness of our new online service, while at the same time cementing the original telephone brand.'