The England and Wales Cricket Board announced his appointment to the leadership role on Saturday, having named Trott in a provisional touring squad in late October.
Warwickshire batsman Trott is targeting a Test comeback after a difficult 12 months.
The 33-year-old batsman has not featured for England since his premature departure from last winter’s Ashes tour, which was attributed to a stress-related illness.
Yorkshire’s Gary Ballance, who would have been a contender to captain the Lions, drops out of the original party as he has been promoted to England’s World Cup squad, who have a tri-series to contest against Australia and India in January.
Cape Town-born Trott will lead England in matches against his native South Africa in Paarl, beginning on January 11, and Bloemfontein, starting a week later.
“Jonathan Trott will captain the 4-day side with a captain for the one-day side to be announced at a later date,” the ECB stated on its website.
Speaking when his inclusion was first announced in October, Trott told BBC Radio 5 Live: “I still have aspirations to play for England. If I do want to play for England again, I have to earn my place back. I had that mentality playing for Warwickshire this year and thoroughly enjoyed my season with them.
“I remember going on previous Lions trips in 2007 and ’08 and I had to prove to the coaches and the ECB set-up that playing for England was something I could do.
“I have to do that again and it’s an exciting time. It’s a good test with regards to where I am and I feel very happy about my cricket at the moment.”
Ben Stokes and Harry Gurney, out of favour for the World Cup, were named on Saturday in the Lions one-day squad for the four-match series that follows the four-day fixtures.