The agreement in the 35-nation UN bloc cleared the way for Panama's formal election to the 15-nation council on Tuesday.
Cesar Mayoral, the Argentine ambassador, told reporters after a closed-door meeting of the group: "It was unanimous."
The deadlock between Venezuela and Guatemala was broken on Wednesday after both countries agreed to withdraw their candidacies for the seat and threw their support behind Panama.
They said that Panama was a geographical meeting point between the north and south of Latin America and had good relations with both countries.
But it took two more days for the Latin American and Caribbean bloc to endorse the move.
Action by the Latin American and Caribbean group was held up so that Caribbean countries could consult their capitals. Before Panama was chosen, speculation had centred on the Dominican Republic, a Caribbean country, as a possible compromise candidate.
'Spirit of understanding'
Ricardo Alberto Arias, Panama's UN ambassador, dismissed suggestions of problems with the Caribbean, saying "it's normal in this organisation to ask for some time to consult".
He said: "We presented our name in a spirit of representing the region.
"It's a spirit of understanding the different conflicts that there are in the world, especially those caused by cultural and religious differences."
The contest between Guatemala and Venezuela went through 47 rounds of balloting in the 192-nation General Assembly before the two countries gave up and agreed on a compromise candidate.
Guatemala led Venezuela by 20 to 30 votes in all but one of those rounds but fell short of the two-thirds majority that is needed.
The US, Russia, Britain, France and China hold five permanent seats on the Security Council. Ten other nations sit on the council for two-year terms with five elected each year.