Mariachi Tenampa's history begins in Santa Fe, New Mexico, located in the Southwest part of the United States. In 1971, Don Miguel Ojeda Sr.-- originally from Carachéo Munícipio de Los Leónes, Mexico-- settled in Santa Fe along with members of his group in hopes of finding better work opportunities. Don Miguel Ojeda Sr. formed and directed this group along with his brothers Elias Ojeda and Antonio Ojeda, his two sons Raul Ojeda and Miguel Ojeda Jr., and 4 additional members. It wasn't long before the local New Mexicans discovered and appreciated this talented group. Mariachi Tenampa quickly gained popularity throughout the state and quickly became known as the best mariachi in the region. The members of this new group had found a new home and were welcomed with open arms into the state of New Mexico, the beautiful "Land of Enchantment".

The name "Tenampa" was chosen while the group performed regularly at a bar called "El Tenampa", located in Santa Fe. This bar was named after the famous "El Tenampa" bar located in Plaza Garibaldi in Mexico City. Plaza Garibaldi is known as the mariachi capital of the world and is the home of hundreds of mariachi musicians who work there at the local bars and restaurants, or who gather there to await drive-by customers to hire them to perform for their festivities.