After a Catholic upbringing and education in New York, Unanue served in the United States Army during World War II, and was awarded the Bronze star for bravery.

He subsequently returned to New York and joined the company his father had founded, Goya Foods.

In 1943, he graduated from high school but, since World War II was in full swing, he was drafted into the United States Army.

[2][3][4][5][6] In 1946, after Unanue returned home, he enrolled in The Catholic University of America in Washington, D.C., where he graduated with a degree in mechanical engineering.

At first, the major supermarkets, such as A&P and Safeways weren't interested in selling anything with the Hispanic demography in mind.

Eventually, with the wave of Hispanic immigrants landing in the United States, the supermarket industry started to take notice.

Under Joseph's leadership, the company became the largest Hispanic–owned food distributor in the United States, with sales of over $800 million a year and with over 2,000 employees.

Goya Foods grew to have more than a dozen facilities in the continental United States, while affiliated companies operate in Puerto Rico, the Dominican Republic, and Spain.

[8] Joseph resided in Alpine, New Jersey with his wife Carmen Ana and continued to participate in civic and cultural activities.