Senegal and Uruguay were also among the five countries that garnered the required votes for council seats during a secret-ballot poll held at the UN General Assembly.
The five countries ran unopposed for the non-permanent seats after regional groups put them forward as their choice, but the contenders still had to garner two-thirds of votes cast.
Applause and cheers broke out in the assembly hall after first results showed Senegal had won the largest share, picking up 187 votes followed by Uruguay with 185.
Ukraine's candidacy had been closely watched amid expectations that sparks will fly with permanent council member Russia, which is accused of supporting separatist rebels in the war in eastern Ukraine.
After the results were announced, Ukrainian President Petro Poroshenko posted a victorious "Yes, we did it!" on his Facebook page.
The vote "opens new possibilities for Ukraine to protect its sovereignty and territorial integrity," he wrote.
Foreign Minister Pavlo Klimkin hailed the result as "a very important day for Ukraine" and stressed that his country "understands the value of peace, struggling under Russian aggression."
The newly-elected members will begin their two-year stint on January 1, replacing Chad, Chile, Jordan, Lithuania and Nigeria.
One of the most experienced non-permanent members, Japan, will be taking its seat for the 11th time as it is locked in an island dispute with China and bristles at Beijing's global role.
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