China has been on a diplomatic offensive since the government of Nobel Peace Prize laureate Aung San Suu Kyi came to power in April, aiming to forge good ties with the resource-rich country.
Suu Kyi visited China in August, where President Xi Jinping told her he wanted to ensure the "correct direction" of relations, and a senior Chinese military officer went to Myanmar last month.
The two warships, the Xiangtan and the Zhoushan, arrived on Friday, and were met by senior Myanmar military officers, the official Xinhua news agency said.
China has been pushing Myanmar to resume work on the Chinese-invested $3.6-billion Myitsone dam project, 90 percent of whose power was originally planned to have gone to China.
In 2011, then-President Thein Sein angered China when he suspended work on the dam, at the confluence of two northern rivers in the Ayeyarwady river basin, over environmental protests.