On Wednesday F1 announced a 2020 Vietnam GP, which is now set to be the first new race under Liberty's ownership.
The wealthy city-state has been hosting F1 races since 2008 and has boosted annual attendance with its Marina Bay Street Circuit race, drawing some 263,000 to the three-day event this year.
"We are delighted to announce that Hanoi will host a Formula 1 Grand Prix", said Carey.
"We value the Silverstone race but we've got to get to a place that works for us".
Earlier this week F1's commercial managing director Sean Bratches hinted that the race could move away from Silverstone, its permanent home since 1987 and a regular F1 venue throughout the championship's history.
China scolds United States over presence in South China Sea
He noted that developing U.S. "Confrontation and conflict between the two militaries will spell disaster for us all". China and the United States have put tariffs on hundreds of billions of dollars of each other's goods and U.S.
"On ongoing negotiations and discussions, we've said in the past this is a sport that seems to like negotiating in public", he said.
For Mercedes to be denied at Sao Paulo's atmospheric Interlagos circuit, Ferrari will have to score 13 points more than Mercedes - a feat they have managed only twice in 19 races so far in 2018. They are very important to Formula 1, and they are very important to fans.
"Most of our grands prix are now half an hour to an hour outside cities, so the race in Hanoi fulfils of one of our preliminary goals - an iconic city hosting racing on a potentially thrilling street circuit".
Ecclestone told Reuters a year ago that he had talks with the Vietnamese about a race while he was in charge but had decided, despite the money on offer, against it because he felt there were enough in that part of the world already.
"Most of our grands prix are now half an hour to an hour outside cities, so this race in Hanoi fulfils one of our preliminary goals - an iconic city hosting racing on a potentially thrilling street circuit".
The Hanoi race will be run on a 5.565-kilometer layout in the west of the city, adding another street race to the existing ones in Monaco, Singapore, Azerbaijan and Melbourne's Albert Park in Australia. A street circuit is a great way to do that.