A tender for the contracts was announced in March - it emerged the account, held by Premier PR since 2000, was being split into two.
BFI head of press and PR Judy Wells told PRWeek the account was divided because of the recent growth of the London Film Festival.
Premier chose not to pitch for either contract, due in part to its "increased slate of work commitments within the international film festival circuit, including Zurich and Macao", the agency said.
Wells added that Premier, which still works with BFI via the UK Film Centre at the Cannes Film Festival, made an "enormous" contribution during its tenure.
The new contracts have each been awarded for an initial period of one year, with an extension of up to four additional years mutually agreed thereafter, Wells said.
DDA's contract, which is worth approximately £110,000 per year, includes handling the PR campaign and red carpet media management for the festival's 12 headline galas, including opening and closing nights, and its special presentation screenings. The agency will also oversee red carpet media management for the BFI's Luminous fundraising gala.
Four Colman Getty's contract, which is worth approximately £140,000 per year, is focused on a PR and publicity campaign for the festival's main programme of 240 feature films. This includes the competitive sections, the London Film Festival Awards and the events programme.
DDA has also been awarded a further contract to handle event production for the London Film Festival gala, following a separate competitive tender process.
BFI has also hired film and festival publicist Mia Farrell to a dedicated six-month, in-house PR role, focusing on the London Film Festival. She will work with Wells and festival director Clare Stewart, as well assist DDA and Four Colman Getty.
The London Film Festival is taking place at various locations throughout the capital between 4 and 15 October.