Smith said Morrell, who will stay as a UK partner at DL&E, will concentrate on growing the business in other regions, such as North America.
Smith said of his new role: "It's a tough time to be taking over, but I'm very excited by the prospect.
I think we have a very good team here."
Smith's previous role as southern regional managing partner will be taken by Neil Morrison.
Cheshire, 45, was a key player in the merger of M&E services firm MGW with DL&E in 1999. His funeral was held on Tuesday.