The 25-year-old joins from Canadian side Atlantic Rock and will feature in the upcoming World Cup before meeting his new club teammates.
Irish coach Toby Booth said he was excited by Sinclair's appearances for his country during this year's Churchill Cup.
"I saw a lot of Jebb during the recent Churchill Cup, and I was impressed," he said.
"His workrate around the park was of a high standard and allowed others around him to shine, and that is what you need from a forward in the Premiership."
London Irish kick off their Aviva Premiership season at home to Harlequins on Saturday, September 3.