Mr Morales said its aim included the study of imperialism and its consequences.
He said it would counteract the Army School of the Americas in Georgia which trained US allies during the Cold War.
Some of its graduates committed serious human rights abuses in the region.
The new academy is based in the city of Santa Cruz in eastern Bolivia and will initially take 100 recruits.
Speaking at the opening ceremony, Bolivia's Defence Minister Reymi Ferreira said: "The School of Anti-Imperialism is a school that seeks to preserve life, unlike the School of the Americas, which brainwashed military officers into believing that the enemy was our people."
He said the training centre would seek to help soldiers identify key threats to the country's national sovereignty.
Since his inauguration in 2005, President Morales has had a relationship with the US which has been at times very tense.
In 2008 he expelled the US ambassador and counter-narcotics agent and more recently he has accused accusing Washington of encouraging "congressional coups" such as the impending impeachment trial of suspended President Dilma Rousseff in Brazil.
He has also accused the US of promoting global terrorism through military interventions, citing the rise of the Islamic State group as an example.
In Latin America, some officers trained at the US-based School of the Americas went on to commit some of the worse human rights abuses in the region.
They include two of the Argentinean military officers who led the junta in the late 1970s.  Human rights organisations say the military government killed around 30,000 left-wing opponents during their administration.
The former Guatemalan President, General Efraim Rios Montt, also trained at  the School of the Americas in the 1950s.
Two Truth Commissions documented widespread human rights abuses by his regime including rape, torture, executions and acts of genocide against the populace, including indigenous population through a scorched earth campaign.
In 2000, the academy at Fort Benning, Georgia, was renamed the Western Hemisphere Institute for Security Cooperation.
The Bolivian President Evo Morales has opened a new military defence academy, which he says will offer courses to counter the influence of the United States in the developing world.