Moreno was born to a Mexican American family in Tucson, Arizona, the oldest of 11 children of Mary and Arturo Ricardo Moreno. His Father ran a small print shop; his grandfather owned Tucson's first Spanish-language newspaper. In 1965, graduated from high school and in 1966, he was drafted into the United States Army and fought in the Vietnam War. After returning to civilian life in 1968, he enrolled at the University of Arizona where he graduated in 1973 with a degree in marketing.

After school, he was hired to work at the Eller Outdoor advertising company. He traveled across the country for the next seven years, relocating several times and in 1984, he moved back to Arizona, settling in Phoenix, where he was hired by billboard company Outdoor Systems.

With baseball being Moreno's favorite pastime, he applied his Business acumen in that arena, as well, purchasing the Salt Lake Trappers minor league team alongside 17 other Investors in 1986. The group owned the team until 1992, and the venture proved to be a resounding financial success.

In 1996, Moreno took Outdoor Systems public. The company's stock soared, and in 1998 Moreno sold the company to Infinity Broadcasting for $8 billion.

In 1997, Moreno and his wife established the Moreno Family Foundation, which supports non-profit organizations focusing on youth and education. It also has provided support to the athletic programs at the University of Arizona.

By 2001, Moreno was hungry to own a Major League Baseball (MLB) team. He attempted to buy controlling interest in his homestate's Arizona Diamondbacks, however no deal could be reached. He nonetheless remained determined to own a Major League team, and soon set his sights on the 2002 World Series champion Anaheim Angels.

In April 2003, it was announced that Moreno had reached a deal with The Walt Disney Company to purchase the team for $180 million. On May 15, 2003, MLB commissioner Bud Selig announced that the sale of the Angels to Moreno had been approved. One of the first people to congratulate Moreno after the news was Diamondbacks' owner Jerry Colangelo, a personal friend who declared it a good opportunity for Moreno.

However, Moreno encountered a substantial backlash from fans of the team, and in particular, from the city leadership of Anaheim, California, over his decision in 2005 to change the name of the team from the Anaheim Angels to the Los Angeles Angels of Anaheim. Moreno saw the change as part of an overall strategy to increase the team's revenue by actively marketing it to, and associating it with, the entire Los Angeles metropolitan area, rather than restricting the team's identity to the city of Anaheim and to Orange County. In recent years, the San Diego Zoo and Los Angeles Times have been notable club sponsors, while all baseball TV rightsholders also use some variation of the team's new name, indicating the effect of Moreno's plan. But the move outraged Anaheim city officials, who responded by suing the team. It also angered a substantial segment of the Angels' fan base in Orange County, who took pride in the team's identity being distinct from Los Angeles. The awkwardness of the of Anaheim suffix, appended to satisfy a contractual requirement for Anaheim to be included in the team's name, also caused the new name to become the subject of national ridicule. Eventually, the team won the lawsuit filed by the city. Whatever displeasure fans felt over the name change has not translated into diminished support for the team, as attendance levels have remained well above 2002 numbers.

On February 26, 2006, Moreno led a partnership of buyers to purchase Radio 830 KMXE, the nation's largest Spanish-language AM radio station. For the 2006 and 2007 seasons Radio 830 KMXE served as the Spanish-language radio broadcast outlet for the Angels. On July 17, 2007 the station began broadcasting from new studios located in Angel Stadium. Just before the 2008 season the station became AM830 KLAA (AM) and went all English language, including the Angels game broadcasts. The station has since added morning and afternoon Sports talk shows to its lineup.

Aside from the name controversy, Moreno's first few seasons as owner of the Angels were largely successful. The team posted three consecutive winning seasons for the first time in club history (2007–2009), including winning the American League Western Division championship in 2004, 2005, 2007, 2008, 2009, and 2014 when they finished with a league leading 99 regular season wins.