His appointment ends 15 months of political crisis which further crippled the already ethnically-divided country in the wake of general elections in October 2010.
In a speech to deputies before the vote Bevanda called on politicians of Bosnia's three main communities -- Muslims, Serbs and Croats -- to "join forces to resolve the economic problems."
"European integration is the only path to the future" for the wartorn Balkans country, he added.
Bevanda, a 55-year-old financial expert and a member of the main Croat HDZ party, was subsequently backed by 31 deputies in Bosnia's 42-seat central parliament.
Only two deputies voted against him while three abstained.
Since the end of the 1992-1995 war Bosnia, one of the poorest countries in Europe, has been divided into two semi-autonomous halves -- the Muslim-Croat Federation and the Serbs' Republika Srpska.
The two entities are linked by a weak central government that will be led by Bevanda.
His nomination was the result of a deal late December between the country's main political leaders after months of wrangling.
Bevanda was finance minister of the Muslim-Croat Federation between 2007 and 2011. Before entering politics the economist worked for several local companies and banks between 1979 and 2007.
He has vowed to make the EU and reviving the flagging economy the key goals of his government.
"Our most important goal is to resume efforts to join the EU," Bevanda said just before he was voted in.
"We have to make the greatest efforts to meet the conditions set" by Brussels.
Bosnia is trailing behind other Western Balkan countries on their EU path. It is the only country in the region that has yet to apply for candidate status in the 27-nation bloc.
To prove their commitment to European integrations local political leaders in December also agreed on two major Brussels-sought laws -- for a census and on the distribution of state aid.
Bosnia will need Bevanda's economic expertise to help lift the country's flagging economy. The International Monetary Fund (IMF) in November forecast growth of just 0.7 percent in 2012 compared to 1.7 percent in 2011.
However Bosnia's central bank governor Kemal Kozaric told news website Beta.ba recently that he predicts a 1.5 percent increase in gross domestic product this year.
"The political crisis which has been going on for six years and the latest impasse since the elections have taken Bosnia to the brink of the social and economic abyss," Srecko Latal, an analyst of the International Crisis Group (ICG) think tank told AFP.
Bosnia's credit ratings were lowered several times in 2011.
Parliament only approved the 2011 budget on December 31, in a last-minute move needed to keep the country's central institutions functioning as of January.
Just hours later, the caretaker government adopted a decree for the budget for the first quarter of 2012.
Bevanda now has 30 days to form his cabinet, which will have nine ministers from the country's three main communities.
Croat parties will name two ministers, Muslims and Serbs will each get three ministries while a final minister will be chosen from other minority groups.
The cabinet will also have to be voted in by parliament after it is officially named by Bosnia's three-man presidency.