Xi met Medina at the opulent Great Hall of the People, where they reviewed Chinese troops before holding talks, a day after treating El Salvador's president to a similar welcome.
During their talks, Medina pledged to support Beijing's "One China Principle" and agreed to participate in Xi's pet trade infrastructure project -- the Belt and Road Initiative -- a Chinese official told reporters.
The leaders also oversaw the signing of 18 agreements, including on infrastructure, investment, finance and civil aviation, the official said, without providing details.
The Dominican Republic abandoned Taiwan in May, as part of a campaign by Beijing to split the self-governed democratic island from its few remaining diplomatic allies.
El Salvador followed suit in August.
Panama's President Juan Carlos Varela, who already met the Chinese leader in Beijing late last year after ditching Taiwan, will attend a massive import expo hosted by Xi in Shanghai next week.
The recent Latin American defections from Taiwan has irked the United States, which recalled its envoys from El Salvador, the Dominican Republic and Panama in September.
Beijing has tried to paint the moves as economic and not motivated by any desire to undermine Taiwan.
The Dominican Republic's choice to switch its allegiance from Taipei to Beijing was "a political decision without any preconditions... The same as with El Salvador and Panama," the Chinese official told reporters.
The new relationship "does not target third parties," he said, reiterating a line the government used following the meeting with El Salvadoran President Salvador Sanchez Ceren on Thursday.
Medina will inaugurate the Dominican Republic's new embassy in Beijing Saturday.
Only 17 countries remain in Taiwan's diplomatic circle as the self-ruling democratic island struggles to fend off Beijing's growing influence around the globe.
China and Taiwan have been governed separately since the end of a civil war on the mainland in 1949, but Beijing sees the island as part of its territory to be brought back into the fold.
Taiwan and China have been engaged for years in a diplomatic tug-of-war in developing countries, with economic support and other aid often used as bargaining chips for diplomatic recognition.
Central America has been a key bastion for Taiwan, with Belize, Guatemala, Honduras and Nicaragua still recognising Taipei rather than Beijing, which has used its economic muscle and promises of investment to entice governments.
The United States recognises Beijing but is congressionally bound to ensure Taiwan's defence, with President Donald Trump's administration especially vocal on defending Taipei diplomatically.
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