Tzafir was born in Tel Aviv and was initially named Tuvia Kozlowski. Tzafir grew up in a traditionalist home of Jewish immigrants from Poland who lived in the Florentin neighborhood in the southern part of Tel Aviv. During the early sixties Tzafir got his big breakthrough when he served in the Nahal military band. Since then Tzafir has become one of the biggest Israeli TV, cinema and stage stars. Through his career Tzafir has participated in numerous entertainment, humor and satire television and stage shows.
In the 1970s Tzafir participated in the successful satire show Nikui Rosh, in which he began performing different imitations of Israeli politicians (such as Yitzhak Rabin, Menachem Begin, etc.). In the 1980s Tzafir appeared many times as a recurring guest on the Israeli entertainment show Siba LeMesiba (סיבה למסיבה) in which he performed many different imitations of Israeli politicians and participated in a variety of comedy skits. In addition, during that period of time he also participated as a guest star in several episodes of the Israeli sitcom Krovim Krovim. In the 1990s Tzafir provided numerous voices for the Israeli satirical puppet show "Chartzufim". In 2004 Tzafir appeared as a guest star in the Israeli daily comical musical drama series "HaShir Shelanu". In 2005 Tzafir appeared as a guest star in the series "Telenovela Ba'am".
Tzafir also starred in several entertainment stage shows, most of which were written by the satirist Ephraim Sidon.
During the 1970s and 1980s Tzafir participated in many Israeli films, among them Salomonico (1972), Charlie Ve'hetzi (1974), Hagiga B'Snuker (1975), Giv'at Halfon Eina Ona (1976), "Eizeh Yofi Shel Tzarot!" (1976), "Ha-Lahaka" (1979), "Nisuin Nusah Tel Aviv" (1979) and "Ha-Instalator" (1986).
During the 1990s Tzafir famously provided the voice of Genie in the Hebrew version of the Disney animated film Aladdin and its two sequels. In 1999, he played the titular character of the straight to video fairy tale medley, Pim Pam Po.
Since the 2000s Tzafir mainly participates in Israeli children's stage shows and children video stories on DVD and video.
In 2008 Tzafir participated in the Israeli drama series Danny Hollywood alongside Gila Almagor.
In the 1960s Tzafir married Yael, who also produces Tzafir's entertainment shows. From this marriage Tzafir has three children, including the successful Israeli film actor and TV director Yoav Tzafir.
In August 2005 an Indictment was filed against Tzafir for violent behavior and threats made against an employee at the production studio of the series "Telenovela Ba'am". In January 2006 the Hashalom court in Jerusalem approved a plea bargain between Tzafir and the State Attorney's Office, according to which he would be given community service.