INTERNASIONAL NEWS - Mr Xi cemented his hold on China for the next five years when he was re-elected leader with no clear successor.
His name and doctrine have been written into the constitution.
The two leaders are due to hold talks at a state visit to China next month, having met at the G20 summit in July.
The pair also discussed North Korea and trade, President Trump said in a tweet. Hours later North Korean leader Kim Jong-un also congratulated Mr Xi.
In the phone call with Mr Trump, Mr Xi expressed a desire to work with the US president to "jointly blueprint future development of China-US ties", Chinese state media report.
China has the world's second-largest economy after the US, its biggest trading partner.
However, relations have been strained by Beijing's territorial disputes in the South China Sea and East China Sea with Washington's allies in East Asia.
Meanwhile North Korean state media agency KCNA reported that leader Kim Jong-un sent a congratulatory message to Mr Xi.
The message "expressed the conviction that the relations between the two parties and the two countries would develop in the interests" of the Chinese and North Koreans.
It also officially acknowledged Mr Xi's political doctrine, noting that the China had "entered the road of building socialism with Chinese characteristics in the new era".
Though relations have cooled in recent years, amid Pyongyang's nuclear and missile tests, China remains North Korea's closest ally.
