The president said the Royal Family had contributed "positively" to co-operation between China and the UK.
Prince William presented him with an official invitation from the Queen to make a state visit later this year.
The meeting in Beijing`s Great Hall of People also saw the two men discuss their mutual love of football.
The prince`s trip will see him promote "brand Britain", highlight the illegal wildlife trade and visit some of the nation`s most famous sites.
The duke is the most senior British royal to visit China since the Queen`s tour of the country in 1986.
Prince Charles has never visited China and he described Chinese officials as "appalling old waxworks" in a leaked diary, written at the time of the Hong Kong handover in 1997.
BBC China editor Carrie Gracie said the meeting between Prince William and the Chinese president symbolised an improvement in the relationship between the two countries. The relationship is now focused on business after a run of political differences over Hong Kong and Tibet, she said.
Speaking through an interpreter, President Xi told the prince: "The British Royal Family holds great influence, not just in the UK but across the world.
"Over the years the Royal Family has shown great interest in, and support for, Chinese/UK relations.
"And members of the Royal Family have done a lot and contributed positively to changes and co-operation between our two countries in areas ranging from trade to environment protection... and cultural exchanges."
He also said the prince`s visit would "surely go a long way to developing mutual understanding and friendly ties between China and British people".
Prince William thanked the president "enormously" for inviting him to the Great Hall of the People and said: "It`s been a long interest of mine, for many years, to come and visit China."
The prince, who is an Aston Villa fan, talked about their mutual love of football.
"I`m looking forward to learning about China`s football," he added.
The first full day of his three-day visit to China also brought a visit to Beijing`s famous Forbidden City, the imperial palace complex of successive Chinese emperors.
While at the British ambassador`s official residence, the prince was tasked with adding the finishing touches to TV cartoon character Shaun the Sheep.
It is one of five sculptures on display in the ambassador`s garden and is part of the Year of Cultural Exchange, a celebration of UK and Chinese creative talent set up by both governments.
The duke also visited a traditional courtyard house, which has been been restored and turned into a museum by charities related to his father, Prince Charles.
Later the prince will fly to Shanghai where he will launch the three-day business exhibition the Great Festival of Creativity, which will promote British innovation and push the benefits of doing business with UK firms.