The Cleveland Cavaliers point guard scored a game-high 26 points as the US thrashed Serbia 129-92 in Sunday's decider in Madrid.
Irving, who was named the tournament MVP, said the World Cup win was a life highlight.
"This is the biggest accomplishment of my life so far," he said.
"We did it with a bunch of guys, we came together on July 27th and we've been together every day since, except for a 10-day period we had off.
"This feels amazing, this is one of the greatest feelings that I've ever felt.
"All the emotions haven't come to me yet but I did it with a bunch of guys I can call my brothers for the rest of my life.
"Being a part of USA basketball allowed me to do that and build relationships that will last a life time. So this is great, to win a gold medal with all these great guys."
James Harden (23 points) also impressed for the US, who joined Yugoslavia as the tournament's most successful nations with five wins.
US coach Mike Krzyzewski praised Irving and Harden, but said his entire team deserved to be lauded.
"Obviously Kyrie and James were amazing, but this has been a great group to work with. They've always wanted to work," he said.
"They were very well prepared and I'm proud of them. There's been a lot of interruptions and they stayed focused on the team they were going to play next."
Krzyzewski's team won the first three quarters of the final convincingly and the coach said it was their most complete performance of the event.
"We had spurts of dominance in a lot of games and we had tough games and then all of a sudden we'd have a spurt and it looked like we dominated," he said.
"Tonight we had about a 35-minute spurt. Tonight we played great. Tonight was a heck of a performance in those last 35 minutes."