Beck helped recruit his successor before leaving to become general counsel at DekaBank at the beginning of this year.
This will be Müller's second spell in Deutsche Börse's legal department. He previously worked for Beck's predecessor, before joining the corporate finance team at HypoVereinsbank three years ago.
In the past three years Deutsche Börse has changed dramatically, growing from 800 staff to around 3,000. Müller will take charge of a legal department that has doubled in size to 46 staff. Deutsche Börse has subsidiaries abroad, and foreign businesses are playing a much bigger role in Germany.
Hengeler Mueller (large, complex transactions), Shearman & Sterling (transactions and cross-border IT contracts) and White & Case Feddersen (corporate law) currently hold the prime positions on Deutsche Börse's legal panel. Arendt & Medernach, Arnold & Porter, Cleary Gottlieb Steen & Hamilton and Freshfields Bruckhaus Deringer are also advisers.