Clinton wound up her visit on Sunday by attending a service at the capital's Beijing Haidian Christian Church and meeting a group of Chinese women.
Clinton held wide-ranging talks with Yang on Saturday, during which she emphasised the need to collaborate on global issues but said little about long-standing concerns over China's human-rights record.
"It is, in our view, imperative that the United States and China co-operate on a range of issues from the economy to global climate change to development and so much else," Clinton told Yang.
"Japan, South Korea and China are uniquely situated to be part of the answer to the problem of global climate change"
She said Washington would press China on human rights but cautioned that this would not keep the two countries from working together on a range of issues such as the financial crisis, and how to respond to the security threats posed by North Korea.
Melissa Chan, Al Jazeera's correspondent in Beijing, said the global financial crisis was high up on the agenda as "the economies [of the two countries] are very closely tied and both of them are struggling".
For his part, Yang said the world faced a series of "major and pressing" challenges.
"The larger situation requires our two countries to strengthen dialogue ... and work together to elevate our relationship to a new level," he said.
Clinton later met Hu Jintao, the Chinese president, and Wen Jiabao, the prime minister.
Her visit to China is the fourth and final leg of a tour of Asia that has also taken her to South Korea, Indonesia and Japan.
It is her first trip abroad as secretary of state.
Human rights fears
Speaking in Seoul on Friday, Clinton stressed while the talks focused on economic concerns "that doesn't mean that questions of Taiwan, Tibet, human rights, the whole range of challenges that we often engage on with the Chinese, are not part of the agenda.
"But we pretty much know what they are going to say."
Human Rights Watch said in a statement that those comments undermined human-rights reform in China and sent the wrong message to the Chinese government.
|Visiting South Korea, Clinton told the North to 'stop insulting and refusing dialogue' [EPA]
The US has long accused China of human-rights abuses and has pressed Beijing to grant greater autonomy to Tibet.
In a 1995 speech in Beijing, Clinton herself openly criticised the country's human-rights record.
On security and counter-terrorism, Clinton had said she was looking for Beijing to take a more active role in convincing North Korea to return to nuclear disarmament talks and ease tensions between Pyongyang, Seoul and Tokyo.
High on the agenda was how to get North Korea to fulfil its commitments to dismantle its nuclear-arms programme.
"What will China be willing to do with respect to the six-party talks and their bilateral relationship with North Korea?" Clinton said.
Washington would not change its policy on Pyongyang as long as it continued "insulting and refusing dialogue" with Seoul, she said.