"He is an extraordinarily competent person, whom I have a very high opinion of," Videgaray said in an interview with the Televisa network.
The links between the two men led to a meeting last summer between candidate Trump and President Enrique Pena Nieto in Mexico City, which caused widespread outrage in Mexico.
Videgaray's hand in the meeting led to his resignation in September as Mexico's finance minister. But after Trump's election, he resurfaced as the nation's top diplomat.
Videgaray also had kind words for Trump, who took to Twitter to praise the former finance minister after his resignation.
"The president-elect was extremely kind and I will always be grateful for those gestures of kindness," Videgaray said. "But that is the past. Now what we must do is act, with the clear exercise of our sovereignty, in what will be a complicated negotiation."
Videgaray will do so without the support of most Mexicans. An opinion poll by the Reforma newspaper said 9 percent of those surveyed supported his appointment as foreign minister.
The bad-cop role will be filled by Economy Minister Ildefonso Guajardo, who is technically the lead NAFTA negotiator under the coordination of Videgaray.
Guajardo said on the same network recently that his office was prepared to file a complaint before the World Trade Organization if Trump imposes a 35 percent tariff on Mexican goods.
He also said the Mexican government would respond to a so-called border adjustment tax, which is supported by some Republicans in the U.S. Congress, by adopting a similar tax in Mexico.
"It's very clear that we have to be prepared to immediately neutralize the impact of this type of measure," Guajardo said.
He also admitted that he had recently read Trump's book The Art of the Deal in preparation for the talks.
"It wasn't one of my priorities last year, but in December it became one of my priorities," he said with a chuckle.
Guajardo's biggest takeaway: "Never sit down at a negotiating table if you don't have leverage."