The appointment follows BT taking on Ed Petter as its new group director of corporate affairs during the summer.
Both hires come after BT announced it would overhaul the governance of Openreach, making it "more independent and transparent" - a move made in response to a recent Ofcom review.
Colloms joined Openreach earlier this month, having spent three years at betting firm Paddy Power, where she was responsible for building and implementing corporate communications and reputational strategy. She had joined in 2013, but left after its merger with Betfair.
Before that, she was a director at the agency Brunswick, where she worked on campaigns for the likes of PepsiCo, Ikea and financial services firm Lehman Brothers.
Colloms will report to Openreach CEO Clive Selley.
BT Group's headquarters are in London and it employs more than 102,000 people globally through its various subsidiaries.