What's the background to the trade war?
The two presidents spoke at length by telephone Saturday, with each expressing satisfaction with trade talks initiated after their meeting earlier this month in Argentina.
The agreement will be "very comprehensive" and will cover "all subjects, areas and points of dispute", the president said in a tweet.
Mr Trump did not offer more detail on what specific progress was being made.
Trump sent his own congratulatory message in return, saying it was his priority to promote cooperative and constructive US-China relations, Xinhua added.
Washington and Beijing imposed tit-for-tat tariffs on more than US$300 billion worth of goods in total two-way trade a year ago, locking them in a conflict that has begun to eat into profits and contributed to stock market plunges.
The two countries are now engaged in a truce in their bitter trade war, holding talks to try and end a dispute that has seen them level increasingly severe tariffs on each others' imports.
"I attach great importance to the development of China-US relations and am willing to work with President Trump to summarise the experience of the development of China-US relations and implement the consensus we have reached in a joint effort to advance China-US relations featuring coordination, cooperation and stability so as to better benefit the two peoples as well as the people of the rest of the world", he said.
China and the United States established diplomatic relations on Jan 1, 1979, with Washington pledging to maintain only non-official ties with Taiwan.
China and the U.S. had made plans for face-to-face consultations over trade in January, China's commerce ministry said last week.
Treasury Secretary Steven Mnuchin last Sunday aimed to allay investor anxiety by announcing that he had held a conference call with major bank CEOs, but the comments were widely criticised by market watchers for raising new doubts.
The year started off on a good foot after President Donald Trump signed off on sweeping tax cuts in December 2017, but quickly turned volatile afterwards.
China has been locked in a bruising trade war with the United States and is also facing a slowing domestic economy. It said the structural reforms include ending China's unfair trade policies and practices with respect to "forced technology transfer, intellectual property protection, non-tariff barriers, cyber intrusions, and cyber theft, services, and agriculture".
"The Chinese and USA economic and trade teams have always maintained close communication", commerce ministry spokesman Gao Feng said at a regular briefing.
Bloomberg News reported on Thursday that a US government delegation will travel to Beijing in the week of January 7 for talks, according to two people familiar with the plans. China's factory activity contracted for the first time in over two years in December, as it seeks to end its bruising trade war with Washington and reduce the risk of a sharper economic slowdown in 2019. "Big progress being made!", Trump said on Twitter.