The deal could turn BT into a telecoms behemoth, since the company would add the UK's most advanced 4G network to its existing fibre broadband network.
The company would have a presence across home broadband, entertainment, mobile and landline services, plus access to EE's current 24.5m customer base.
BT said it expects to generate revenue by selling into EE customers who don't already use its consumer and business services, and said it sees "significant synergies" with EE's back-end infrastructure.
If approved, the deal would furnish Orange with a 4% stake in BT, and Deutsche Telekom a 12% stake and a position on BT's board, with the rest paid in cash.
BT turns down O2
The trio are currently in "exclusive discussions" meaning the deal could yet fall through. BT could also face regulatory hurdles, since the company leads the market in home broadband, and EE is the UK's biggest mobile operator.
BT had also confirmed acquisition talks with EE's rival, Telefonica-owned O2, with Telefonica's chairman even flying to London in the hopes of clinching a twelfth-hour deal. An O2 spokeswoman refused to comment on the deal.
CCS Insight analyst Paolo Pescatore said EE had likely won out because of its strength in 4G - and its own aspirations to enter the entertainment market.
He said: "We consider EE to be a more desirable asset for BT to own than O2 and thus view its move as a major statement of intent regarding its multi-play aspirations.
"BT’s move reflects the company’s strong ambitions in multi-play and serves as a clear warning to UK rivals, notably Vodafone, Sky and Virgin Media. These companies will be forced to review their position as the market for convergence in the UK rapidly comes to the boil."
Pescatore added that the UK's industry watchdog, Ofcom, was unlikely to block the deal but could force BT to demerge its Openreach and Wholesale arms.