Baglee's promotion fills the gap left when the role, then held jointly by Lu Dixon and Trevor Chambers, was axed in November.
Baglee was selected from a list of four creative directors at the agency. The other candidates were Kate Pybus, Graham Dexter and Nigel Clifton. They will remain at the agency in their roles as creative directors.
In his new position, Baglee will run a team of 30 people working across EHS Brann's digital and direct marketing accounts.
Baglee joined EHS Brann as a copywriter when it merged with Realtime in 2001. Since then, he has worked as the creative director on a number of accounts, including British Gas, Diesel, Buzz and COI. He was made a partner in 2002 and a board director in 2003.
During his time at the agency he has won awards including a gold at the Campaign Digital Awards in 2005 for Diesels Dreams and a Direct Marketing Association Awards gold for the Diesel Joanna website in 2000.
Matt Atkinson, the chief executive of EHS Brann, said: "I am delighted that Patrick has agreed to take the helm. Patrick brings real depth to the department. He's part planner, part ideas junkie, a wonderful team builder and has a wonderful style and charm.
"But perhaps more importantly, he has the ability to take good work and make it great - something we are committed to doing for all of our clients."
Baglee said: "It's great to take the helm."
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