Timms will pick up from where Lord Carter, the former Ofcom chief executive, who leaves during the summer recess.
His departure was confirmed in June when he presented his final report into the future of the nation's communication industries.
Carter's recommendations include a £6 per year levy on all phone lines to fund the rollout of faster broadband connections across the UK, but failed to make any definitive decision on the future of Channel 4's funding.
Timms is currently treasury minister and is the MP for East Ham.
The Number 10 press office was unable to confirm the appointment but did not deny the reports.
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