Mr Kirby had been seen as a future chief executive of American Airlines, but instead will move straight into his new job at United.
American Airlines is giving him more than $13m (Â£10m) in severance pay.
United's financial performance has been lagging behind competitors and Mr Kirby's appointment will bring extra experience to the management team.
Last summer, United chief executive Jeff Smisek stepped down amid a corruption investigation.
A few months later, United's board faced a leadership challenge from two activist hedge funds.
United's current chief executive Oscar Munoz is also considered an industry newcomer and has been struggling with health issues following a heart attack last year.
"Scott is a proven leader, whose deep airline experience and expertise will further accelerate our efforts to build the best airline in the industry," Mr Munoz said in a statement.
"Scott's appointment, along with other recent leadership announcements, is the culmination of the formation of my senior leadership team".
Mr Kirby played a key part in the 2005 combination of America West and US Airways, as well as the 2013 merger of American and US Airways.
American Airlines president Scott Kirby is moving to rival United Continental to take up the same job.