Maxus already handled the BT and Plusnet brands, worth upwards of £100m a year, while MEC looked after EE, worth in the region of £60m. BT bought EE for £12.5bn in January.
The new unit will be based at Maxus’ offices at Finsbury Square in East London and involve around 60 staff, some of which will relocate from MEC’s South Bank premises.
Group M won the account after a competitive pitch, involving an unknown number of agencies.
Zaid Al-Qassab, chief brand and marketing officer for BT Group, said that while the move was intended to allow for closer working between the teams, it would not impact the strategy of each brand.
There are also no plans to review the creative accounts for either BT, held by Abbott Mead Vickers BBDO, or EE, which is with Saatchi & Saatchi. "We intend to keep all three of our consumer brands and that is still the case," said Al-Qassab.
When BT completed its acquisition of EE, there was speculation it could lead to the demise of the four-year-old brand, created to replace Orange and T Mobile when the network launched its 4G service in 2012.
At the time, BT chief executive Gavin Patterson denied this would happen "in the short term", but refused to rule out it happening eventually.
BT has already made a guest appearance in EE's latest campaign, which promotes the BT Sport app being offered to EE customers for free for six months.
The head of the new operation, who has not been identified yet, will report to Maxus chief executive Nick Baughan. While a number of details are still to be finalised, Baughan said that Team Connect should be up and running during the fourth quarter of 2016.
"To meet the ambitions of BT Group we’ve combined the best of Maxus and MEC to create Team Connect," said Baughan. "BT exists at the high-speed intersection of media, content and telecommunications and by bringing our talent and our resources together we can deliver real and lasting competitive advantage to the Group."