Hodges, who is currently the producer of the Criterion Theatre in the West End and previously founded new writing theatre company HighTide, will instigate a "producer-led model" at Nuffield.
Sandford has been artistic director of the venue for 25 years. According to press, he and Anderson "have presided over the Nuffield's growth from an in-house producer of acclaimed new plays, and neglected classics, to a broader remit incorporating a series of exciting collaborations across new spaces and venues."
During their tenure the Nuffield has collaborated with companies including Cheek by Jowl, Frantic Assembly, Derevo, Peter Brook's Theatre des Bouffes du Nord, Out of Joint, Crying Out Loud, the National Theatre and Clod Ensemble.
In 2011 they were jointly awarded the City of Southampton Award for their services to the city, and Sandford was awarded an Honorary Doctorate from The University of Winchester.
In his final season Sandford will direct a major revival of Yasmina Reza's God of Carnage starring Matthew Kelly, and a new play Smallholding by Chris Dunkley. The season also includes co-productions with HighTide Festival Theatre and Headlong Theatre.
In a joint statement Kate Anderson and Patrick Sandford described running the Nuffield as "a real privilege", adding "we are delighted that Sam, a terrifically talented theatre maker himself, is taking on the leadership of the company."
Hodges, who will become creative and executive director & CEO, said: "I am thrilled to be leading the Nuffield Theatre at such an important time of development and growth for both the company and the city of Southampton. Despite these being uncertain times for regional theatres across the country, the Nuffield is a terrific theatre supported by a brilliant and passionate team of people, making it an exciting challenge, as a programmer, as a producer and as a director."