Weir played in the biennial contest against the United States five times, most notably beating Tiger Woods in their singles match at Royal Montreal in 2007.
"Presidents Cup has become such a big part of my career, so to be here in this moment announced as captain of the 2024 International Team is surreal," said Weir.
"When I look back, I have so many incredible memories associated with this event whether it be my debut in 2000; winning my Singles match against Tiger in 2007 at Royal Montreal; witnessing Ernie create the shield in 2019; and then seeing Trevor carry that momentum in 2022.
Now as I look with anticipation toward 2024, I couldn't be more excited to lead the International Team into my home country of Canada for what will surely be the experience of a lifetime."
The left-hander, who has also been an assistant captain in the last three editions of the event, added: "Captaining the team at this golf course is going to carve out an entire new piece of history in my career that can't be replaced.
"I have such a deep sense of pride bringing the team home knowing that, in my opinion, the people of Canada are the most loyal and passionate sports fans in the world.
The International Team has won just one of the 14 Presidents Cups staged to date.