BEIJING—Cleared to stay in power indefinitely, Chinese President Xi Jinping has discarded the leadership structure he inherited and is kicking off his second term with a handpicked team of trusted lieutenants.

For the next five years, Mr. Xi will look to his inner circle to shore up a sluggish economy, eradicate poverty and enhance China’s global standing—while shielding his ambitious agenda from being derailed by rocky relations with the U.S.

Two men in particular have emerged in key roles: Wang Qishan, the former anticorruption chief who took office as deputy head of state Saturday, and Liu He, the architect of Mr. Xi’s economic policies, who was promoted to vice premier Monday.

In recent weeks, Mr. Xi and his two deputies met directly with U.S. officials, people familiar with the matter say—a sign of the president’s heightened concerns about China-U.S. ties.

Mr. Xi hosted the U.S. ambassador to Beijing, Terry Branstad, at an informal gathering of both men’s families in early February, according to people with knowledge of the event. The two have known each other since Mr. Xi visited the U.S. in 1985.