The agency won the account, previously handled by Fallon, following its appointment to run European direct marketing for Callaway in February.
Fallon, which was appointed in 2000, stopped working for Callaway last year. Claydon Heeley's direct marketing has included an insert and in-store campaign featuring the golfer Seve Ballesteros.
Claydon Heeley's activity will cover all media, including TV and digital.
Key markets include the UK, Germany, Spain, Sweden and France.
Chas Sharp, the marketing manager of Callaway Golf Europe, said: "Claydon Heeley has won the advertising account on the strength of the excellent creative and planning that it has done for Callaway to date."
Callaway is the world's leading golf club manufacturer with global sales of more than £500 million. It produces the Big Bertha range of drivers and the Odyssey putters. It also produces the HX golf balls.
US activity remains with Omnicom's US affiliate of Claydon Heeley, Direct Partners. The Allmond Partnership handles UK media.