Ansin was born to a Jewish family, in Worcester, Massachusetts and raised in nearby Athol, Massachusetts. In 1936, his Father, Sidney D. Ansin, the son of a Ukrainian immigrant, founded Anwelt Shoe, a shoe Manufacturing Business in Fitchburg, Massachusetts and in 1941, he moved the family to Florida. Utilizing the steady cash flows from his Manufacturing operations in Massachusetts, he soon made a small fortune in real estate. His parents were the founding members of Temple Beth Sholom in Miami Beach. Ansin was sent back to Massachusetts for preparatory school at Andover Academy and, after two years at Harvard University, he graduated in 1957 from the University of Pennsylvania with a BS in Economics. His brother is former Massachusetts commerce commissioner, Ronald Ansin. Ronald bought Anwelt Shoe from his Father in 1966.

In 1962, after his Father purchased the license for Miami's WSVN Channel 7 for $3.4 million, then an NBC affiliate, Ansin became an executive vice President at Sunbeam Television Corp, the holding company for the television station. After his father's death in 1971, he became Sunbeam's President. In 1988, WSVN lost its affiliation with NBC and Ansin, after rebuking then CBS chairman Laurence Tisch's offer to purchase the station, found himself without network sponsorship. The station affiliated with the up-start Fox Network and pulled down supplemental news broadcasts from the newly launched CNN satellite network. Rather than follow the conventional approach used by successful independent stations (morning kids' shows, afternoon game shows, evening movies, and syndicated sitcoms), Ansin instead decided to focus on news. Instead of dry and stoic presentation, he and his news Director, Joel Cheatwood, created the now ubiquitous Miami News Style with fast-paced reporting, crime-lead stories, live breaking coverage, and pretty presenters. “If it bleeds, it leads” became an industry catch phrase. The approach was wildly successful and WSVN news soon became the market leader. WSVN reported $96 million in revenues in 2011

In 1993, returning to his childhood home, he bought Boston's WHDH Channel 7 in 1993. He implemented a less tabloid style than in Miami but still shortened the time spent on individual news stories, relied heavily on video and audio effects, and emphasized "on-the-spot" reporting. “When you finished watching a half-hour of Channel 7 news, you were excited as hell, but you couldn't remember what the news stories were.” In 2006, Sunbeam Television purchased Boston's WLVI, a CW Television Network affiliate, from Tribune Broadcasting.