Mesa offered to resign after weeks of crippling street protests that threatened to paralyze the South American country. Troops shot and killed a protester on Thursday.
The job of interim president automatically went to Rodriguez after two congressional leaders, who were first and second in line for the post, turned it down.
Elections are expected in the next three to six months. Mesa's term was to have ended in August 2007.
Congressional lawmakers met in an emergency session in the historic colonial capital of Sucre Thursday to accept Mesa's resignation and swear in Rodriguez.
Protests earlier forced Congress to suspend proceedings as the armed forces chief threatened military intervention.
Hundreds of miners and farmers clashed with riot police outside the whitewashed hall where the session was to have been held.
The naming of an interim president meets the protesters' demand that Mesa step down.
But other issues, such as the nationalization of the oil and gas industry and the formation of a new constituent assembly to rewrite the constitution, were still unmet, journalist Noah Rudovsky told CNN.
He said it was unclear whether demonstrations would continue.
Weeks of blockade have nearly paralyzed the capital of La Paz where nearly two million residents live, with gas stations closed, supermarkets empty and drinking water scarce.
"I think his [the new president's] job at this point mainly is to bring the nation together if he can to bring an end to the roadblock and to pave the way for a peaceful election within the next three to six months," Rudovsky said.
The protesters -- largely members of the country's Indian population -- also seek a more even distribution of wealth.
Bolivia, with a population of 9 million, has long been one of South America's poorest countries and a major recipient of international aid.
The protests grew after Bolivia's Congress moved last month to raise taxes on foreign oil companies that have flocked to the country to develop its natural gas reserves -- the second largest in South America after Venezuela.
The measure was intended to calm street tensions, but it only unleashed new street protests in a nation where anti-globalization anger is high.
Mesa took office in October 2003 when a bloody popular revolt over free-market economic policies forced his predecessor, former president Gonzalo Sanchez de Lozada, to flee the country.
Bolivia has a history of unrest.
Since breaking away from Spanish rule in 1825, it has been beset by nearly 200 coups and counter-coups.