The agency was hired following a six-way pitch overseen by Callaway marketing director Jeff Dodds, who joined the company from Honda earlier this summer.
The business moves from start-up agency Amp London, which had itself won the work from Young & Rubicam in March.
Nexus/H will adapt TV ads from the US and create press, in-store, point-of-sale, direct mail and digital activity.
Manning Gottlieb OMD, which handles Callaway's media, is not affected by the appointment.