Weir has also selected South Africa's Christiaan Bezuidenhout, Canada's Corey Conners, Taylor Pendrith and Mackenzie Hughes, South Korea's Si Woo Kim alongside Australia's 26-year-old Lee as the Cup returns to Royal Montreal Golf Club for the the week of September 24-29.
Kim's fellow Australians Adam Scott and former world No.1 Jason Day were among the six automatic qualifiers for the event to join Hideki Matsuyama, Sungjae Im, Tom Kim and Byeong Hun An in Weir's line-up.
This is the also first time three Canadian players will compete for the International team, which is looking for its first victory over the United States since 1998.
On selecting Lee, Weir told PGA.com: "As one of the most popular players on the PGA TOUR, Min Woo is going to be an incredible addition to the International Team and our passionate fans in Montreal.
"He is one of the best drivers of the golf ball on the PGA TOUR, and I can't wait to let him cook at the Presidents Cup in a few weeks."
United States captain Jim Furyk picked the players ranked seventh to 12th in the points standings as his wild cards, including assistant captain Keegan Bradley.
Bradley, who will also captain the Ryder Cup side next year, is joined in the team by Sam Burns, Tony Finau, Russell Henley, Brian Harman and Max Homa.
"When I named Keegan as a captain's assistant for the Presidents Cup, I knew there was a chance he would play his way onto the US team, and I can say without a doubt he did just that," Furyk said.
"The grit he showed in the final round in Memphis, followed by the win in Denver, exemplified the competitive nature he has always played with, and I know he will bring that same fire to Royal Montreal in a few weeks."
The International Team has won just once in Presidents Cup history, with the United States claiming 12 victories and the 2003 edition ending in a tie.
