Niger, Tunisia and Vietnam also won two-year terms, and the five countries will take their new spots next year on the 15-member council.
"An historic occasion," St. Vincent and the Grenadines Prime Minister Ralph Gonsalves said after his country became one of the smallest ever elected to the council. Vincentians hope to work on addressing "the security consequences of adverse climate change," among other concerns, Gonsalves said.
The council has five permanent members with veto power: China, France, Russia, the United Kingdom and the United States.
Other members are elected by the assembly's 193 states for staggered, two-year terms. Five are chosen each year.
Equatorial Guinea, Ivory Coast, Kuwait, Peru and Poland are finishing their terms this year. Belgium, the Dominican Republic, Germany, Indonesia and South Africa will remain on the council through the end of 2020.
The coveted seats are allocated by global regions. Countries often plan for years to campaign for a spot, which can raise a nation's profile in international affairs and afford it a strong voice on the world's most pressing peace and security issues.
The council also provides a platform for bringing up international topics of particular concern to those who hold seats at the horseshoe-shaped table.
"It was an effort of 14 years to arrive here, and we are extremely grateful," Estonian President Kersti Kaljulaid said after her country vied with Romania through two rounds of voting for an Eastern European seat. A 2/3 majority is necessary to win.
Estonia's priorities include cybersecurity, promoting principles of international law and making the council more transparent and efficient, Foreign Minister Urmas Reinsalu said.
Tunisia has served on the council three times, most recently in 2000-2001. Niger had a term in the 1980s, and Vietnam in 2008-2009.