The political situation in Lebanon is fragile too, with the Western-backed majority in parliament and Hizbullah and its allies still deadlocked on forming a new unity government following June 7 elections.
But Lebanon's UN Ambassador Nawaf Salam said his country "believes it has a special mission as a country of tolerance and diversity".
"We hope that our seat on the Security Council will help us also promote not only rule of law but dialogue of culture and civilization and will help us work for a more just and more democratic international system," he said.
Lebanon has not been a member since 1953-54, but Bosnia has never been on the council at all.
Bosnian Foreign Minister Sven Alkalaj said his country's experience during war "will be an important asset for the Security Council and for the United Nations system".
"Preventive diplomacy is something we will be working very much on - never to allow the crisis and loss of human life to happen ever again as we experienced in Bosnia," he said.
Britain's UN Ambassador John Sawers welcomed the fact that the Security Council would have new members that had been on the receiving-end of UN military deployments.
"We have two countries in Lebanon and Bosnia that have been through conflict and can bring their own national experiences to the Security Council.
"I think also for both those countries, the experience of being on the council will help strengthen their national government systems ... and broaden the context of those governments," Sawers said.