On November 18, the purpose-built venue will host the first US Grand Prix since Indianapolis in 2007.
"It's very green, as you could expect," Andretti, the 1978 Formula One world champion, told Reuters. "You get offline a bit - it's a bit slippery. But that's normal for a new circuit. Overall, my impression is absolutely fantastic."
Texas elected officials and actor Patrick Dempsey, who competes in the GRAND-AM Rolex Sports Car Series, were on hand for the first-lap ceremony on a hot, sunny afternoon.
Andretti, a Circuit of the Americas ambassador, ceremonially cut a ribbon of chequered flags from a Lotus 79 Cosworth racing car and then zoomed up a steep hill toward the hairpin Turn 1.
"That's my designated signature corner," said Andretti, who had initially been scheduled to drive a Lotus R30 Formula 1 car before that plan was aborted because of a mechanical problem.
"I think that's going to invite quite a bit of action there, a lot of overtaking for sure."
Andretti, who has won races in Formula One, IndyCar, the World Sportscar Championship and NASCAR, said going up a hill and braking often gave drivers a false sense of security.
"So you're going to push the envelope," the 72-year-old added. "If you're going to challenge, that's the time you're going to do it. The track seems to be, in many of the braking areas, wide enough to invite that.
"If you somehow misjudge a situation, I think you can get out of it because of the width. I think you're going to see a lot of action because of that, and that's what it's all about."
Construction workers in hard hats were busy at the site on Sunday, and Circuit of the Americas officials said the work remaining involved landscaping and finishing building interiors.
"Everything is ready for hosting a race," Circuit of the Americas spokeswoman Ali Putnam said.
Teams are eager to return to a country that is a key market for sponsors and car manufacturers but one that the sport has found hard to crack over the years.
Next year's inaugural Grand Prix of America in New Jersey will be postponed to 2014 because local organisers need more time to prepare, Formula One supremo Bernie Ecclestone said on Friday.
Andretti said he had spoken with some of those involved in the New Jersey race.
"They just have a few issues here and there, which I think pushed the project back, but they're still very much just going for it," Andretti said.
"I know there potentially were some negative comments and so forth going on, but you know, they're pressing on."
Having two races in the United States would help build a fan base in the country, Andretti said.
"To me, the more the merrier," he added. "If there's going to be any country that would host two races and justify it, in my opinion, I think it would be the US."