Dong's appointment was announced by China's top legislators at a Standing Committee meeting of the National People's Congress in Beijing on Friday.
The move follows a slew of dismissals of top military officials from the country's top posts earlier this year.
As well as Li, it included the removal of Qin Gang as foreign minister in July. No reasons were given for Li or Qin's dismissals. Both had been in their posts for only seven months respectively.
Further sackings took place this week too, with nine senior military officials removed from the Standing Committee on Friday.
Three executives at state-owned missile defense firms were also removed from Beijing's top political advisory body earlier this week.
Some analysts say this could indicate that a possible wider purge has taken place, targeting senior military leaders.
Dong was made commander of the navy in August 2021. His previous roles included serving as deputy commander of the Chinese military's Southern Theatre Command. Its area of operations includes the South China Sea - a disputed area, over large parts of which China claims sovereignty.
Dong's appointment comes after military personnel from China and the United States held their first high-level talks by phone in more than a year last week.
Relations between the two nations soured in 2022 after the then US House Speaker Nancy Pelosi visited Taiwan. Taiwan is self-ruled, but China sees it as a breakaway province that will eventually unite with it.
In recent months, there has been a rapprochement between China and the US, with Chinese President Xi Jinping meeting his counterpart Joe Biden in California in November and agreeing to resume military communications. The two had not spoken for more than a year.
