The mobile giant will not replace him directly and will instead split the reporting lines for the marketing and comms teams from 1 January.
The comms team will report into chief corporate & strategy officer Stephen Harris and the brand team will report into chief consumer marketing officer Pippa Dunn.
Day was praised for his "pivotal role in the successful launch of EE" by his CEO Olaf Swantee.
"With his strong internal and partner teams, Steven created a brand that has become synonymous with innovation," Swantee added.
Day was with Orange as chief of staff, brand and communications, before the merger of the France Telecom-owned company with T-Mobile in 2010.
