The decision came late at night after a congressional meeting set for earlier Thursday was cancelled after police and protesters clashed near the site of the session in Bolivia's historic capital Sucre, leaving one demonstrator dead.
Rodriguez was actually third in line to assume the presidency, but Senate President Hormando Vaca Diez and Congress President Mario Cossio Cortez both declined the position.
In an address to lawmakers and Bolivians, Rodriguez thanked leaders for their faith in him and said Bolivia had a way to go to repair the damage to the nation.
"We must now work to restore the republic," said Rodriguez shortly after midnight Friday.
Rodriquez faces a tough job in appeasing Bolivian protesters, enraged with the previous government's handling of its gas industry and calling for its nationalization.
Protesters are calling for a new constitution to give Bolivia's indigenous people more representation in the government. They are also condemning a call by eastern gas-rich provinces to become more autonomous.