Wright married his first wife, Juliette Gale, in 1964. She had been a singer in one of the early bands that evolved into Pink Floyd. They had two children and divorced in 1982. His second marriage to Franka lasted between 1984 and 1994. Wright married his third wife Mildred "Millie" Hobbs in 1995, with whom he had a son, Ben. Wright's 1996 solo album Broken China is about her battle with depression. They separated in 2007. Wright's daughter Gala was married to Floyd and Gilmour touring bassist Guy Pratt.
Wright had been fond of the Greek islands since a sabbatical visit in 1964, before Pink Floyd were formed. He moved to Greece in 1984 after the Zee project, briefly retiring from music, and enjoyed sailing and yachting. In his later years, Wright lived in Le Rouret, France, and spent time on a yacht he owned in the Virgin Islands. He found sailing therapeutic, relieving him from the pressures of the music business. He was also a collector of Persian rugs.