In 2000, the Russian Orthodox Church canonised the royal family, saying they had undergone suffering with gentleness, patience and humility.
Citing preliminary forensic and DNA tests, the deputy forensic chief scientist in the Sverdlovsk region said the appearance, age and sex of the remains they found mean it was "highly probable" they belonged to Alexei and Maria.
"On the basis of the expert analysis, it is possible to conclude with a large degree of certainty that parts of the skeleton... belong to Tsarevich Alexei and his sister, Grand Duchess Maria Nikolayevna Romanova", he told Russian media.
The BBC's James Rodgers in Moscow says the whereabouts of the missing Romanov children has been one of the great unsolved mysteries of Russia's blood-soaked revolution.
After they were shot, the bodies of the tsar and the remainder of his family were burned, doused with acid and thrown into a pit.
They were exhumed in 1991, after the collapse of the Soviet Union.
Final identification of the rest of their family took years, and they were ceremonially buried at the St Peter and Paul Cathedral in St Petersburg in 1998.
Even since then, some members of the Russian Orthodox Church have continued to question the scientists' conclusions, our correspondent says.