A small park existed near the intersection of Merida Street and Barclay Avenue as early as the 1920s. An undated inventory of San Antonio parks believed to be from that period lists Crockett Heights Park, named for the surrounding subdivision. By 1932, the park had been renamed Edgewood Park, probably to avoid confusion with two other city facilities, Crockett Square and Crockett Street playground. Originally less than one acre in size, Edgewood Park was enlarged in the early 1970s in conjunction with the Model Cities program to include 7.7 acres and was redeveloped using Bureau of Outdoor Recreation and 1970 bond funds.
In 1976, City Councilman Richard Teniente initiated a move to name the park for Juan Vidaurri who had lived just across the street and worked to improve the neighborhood for many years. Vidaurri was born in 1905 in Musquiz, Mexico and emigrated to the United States with his parents in 1915 during the Mexican Revolution. He became known for his political and civic work and was called by many "El Viejito" and "Don Juanito." It was said that his house served as a combination community center and political command post. Vidaurri founded and became president of the civic organization known as "Amistad" dedicated to strengthening ties between the United States and Mexico.
Among his many friends was Governor Dolph Briscoe who appointed Vidaurri as Ambassador of Goodwill of the State of Texas in 1975. Briscoe attended the ceremony to rededicate Edgewood Park in Vidaurri’s name on July 23, 1977. Also attending was Texas Secretary of State, Mark White, and Oscar Flores Tapia, governor of the state of Coahuila, Mexico. Vidaurri remained active until late in his life, and died in San Antonio at age 85 on September 6, 1990.
A new playground, park toilets, and ADA modifications were constructed in Vidaurri Park in 2001 using funds from the 1994 bond election.