"The navy ships in Crimea have been taken. Despite the fact that commanders were given orders to use their arms, they did not use them to avoid bloodshed," Ukrainian Defence Minister Igor Teniuj said.
The Konstantin Olshansky and the minesweeper Cherkassy were the last Ukrainian ships to ignore orders to surrender from the Russian military in the waters of Donuzlav Bay.
Russian forces sank two Ukrainian vessels, preventing the two warships from escaping.
The Konstantin Olshansky went on full combat alert Sunday after boats carrying Russian marines approached.
"Olshansky has all its armaments and the sailors have firearms," Teniuj said in response to media reports that the crew was unarmed.
Russian President Vladimir Putin and the leader of the breakaway Ukrainian region of Crimea signed a pact last Tuesday making the Black Sea peninsula part of Russia again.
The accord came after more than 96 percent of Crimeans who cast ballots in last Sunday's referendum on rejoining Russia voted "yes."
Ethnic Russians make up around 60 percent of the roughly 2 million residents of the peninsula, which then-Soviet leader Nikita Khrushchev decided to make part of Ukraine in 1954.
Moscow has deployed troops in the peninsula, claiming it was protecting ethnic Russians and Russia's interests.
The US and its allies denounced Sunday's referendum in the Crimea as contrary to international law.