The letter thanked Xi for his congratulatory note on Trump's inauguration and wished the Chinese people a prosperous Lunar New Year of the Rooster, the White House said in a statement Wednesday.
"President Trump stated that he looks forward to working with President Xi to develop a constructive relationship that benefits both the United States and China," it said, Reuters reported.
China said Thursday it attached great importance to China-US ties after confirming it received the letter.
At a daily press briefing in Beijing, Chinese Foreign Ministry spokesman Lu Kang said China commended Trump for sending Lunar New Year greetings to the Chinese people and said cooperation between the two countries was the only option.
Trump and Xi have yet to speak directly since Trump took office on Jan. 20, although they did talk soon after Trump won the US presidential election in November.
Diplomatic sources in Beijing say China has been nervous about Xi being left humiliated in the event a call with Trump goes wrong and the details are leaked to the US media.
Last week, US ties with staunch ally Australia became strained after the Washington Post published details about an acrimonious phone call between Trump and Prime Minister Malcolm Turnbull.
"That is the last thing China wants," a source familiar with China's thinking on relations with the United States told Reuters. "It would be incredibly embarrassing for President Xi and for Chinese people, who value the concept of face."
A senior non-US Western diplomat said China was unlikely to be in a rush to set up such a call.
"These things need to happen in a very controlled environment for China, and China can't guarantee that with the unpredictable Trump," the diplomat said.
"Trump also seems too distracted with other issues at the moment to give too much attention to China."