Goldberg was the color commentator for the Miami Dolphins football games for 610 WIOD AM, and hosted his own afternoon drive show on the station. In 1992, following weeks of Hurricane Andrew aftermath that dominated all the local market stations, Goldberg opted to interview guests Dolphins coach Don Shula to talk football and novelist/screenwriter Elmore Leonard when WIOD's program director insisted he talk only about Hurricane Andrew, three weeks after the storm. His reasoning was to allow listeners that were tired of the morbid aftermath talk looking to move on or for a distraction on different subjects. He was then immediately fired by the station and replaced by former Miami Dolphin Jim Mandich. Goldberg then moved to 560 WQAM, which had recently changed over to an all-sports format.
Goldberg was formerly the host of an afternoon-drive show on 560 WQAM radio in Miami, which aired from 4pm to 7pm weekdays. He would be moved around on the WQAM programming schedule over the years with an extended period hosting a show from 2pm to 6pm weekdays, having long-time Miami radio host Neil Rogers as a lead-in. Goldberg would also serve as the morning-drive host (6am to 10am) for a short time after Howard Stern left terrestrial radio and was therefore no longer on WQAM. Goldberg left WQAM on Dec 31, 2007 when his contract expired.
During the football season, and before certain major horse racing events, he also appears nationally on ESPN television and radio. During these segments, he analyzes the odds for football games and horse races and makes predictions based on them. For football, these predictions on always made on the Sportscenter that immediately precedes the ESPN show Sunday NFL Countdown. The Sportscenter anchors converse with Goldberg by referring to him as "Hammerin' Hank". They give a brief lead in to a game where Goldberg then takes over and provides brief analysis of the game from a bettor's standpoint. A graphic then soon appears with Goldberg's prediction as to which NFL team will win the game, and with an indicator (generally a checkmark V) as to which team will cover the spread. Pro football is the biggest betting sport in the United States, with total wagers now running more than $1 billion a week. The average bettor, despite all the touts and information, loses season after season. The late Bob Martin, manager of Las Vegas’s first casino sportsbook, is quoted as having stated that the number of bettors who win betting pro football is so small that “it is virtually the same as if no one won.” 
Criticism levied against ESPN from several sources cites ESPN's official position is that of a news organization, and as a news organization they are not supposed to engage in activities such as promoting any form of prognosticating for NFL games which promote the often illegal activity of gambling.