Zalmay Khalilzad, the US ambassador to the UN and the current president of the Security Council, said: "I was particularly heartened by the election of Bosnia."
He added that he he had been "particularly concerned" by the prospect of Belarus being chosen.
"This was the right decision," he told reporters.
In the only other contested part of the election - for two vacant West European seats - the Netherlands and Italy went through at the expense of Denmark.
Uncontested elections for African, Asian and Latin American seats gave places on the council to Angola, Bolivia, Egypt, India, Indonesia, Madagascar, Nicaragua, Philippines, Qatar and South Africa.
The remaining seats on the council are not up for election this year.
The council was created in March 2006 to replace the discredited Human Rights Commission, and one aim was to keep some of the worst human rights offenders out of its membership.
Last year, the council adopted eight resolutions criticising Israel for its military actions in the Palestinian territories and Lebanon.
The only other country to be criticised was Sudan. Censure by the council brings no penalties beyond international attention.