Using a harsher tone than in last year's speech, Cinping said he was "confident" that the island would rejoin China.
Taiwan will hold a critical election on January 13 that will determine the island state's China policy for the next four years.
Taiwanese President Tsai Ing-wen also said in her New Year's speech that "the will of the nation should determine" the island's relations with China. Tsai's government has repeatedly said that China is trying to interfere in Taiwan's elections to ensure that leaders close to Beijing are elected.
While Cinping's messages were in line with his stance that Taiwan should come under the Chinese flag, the message was harsher than last year. "The two nations on both sides of the Taiwan Strait belong to the same family," the Chinese leader said last year.