Isa Nacewa captained the Pro14 champions last term but Sexton has been named as his successor after he retired for the second time at the end of 2017-18.
Sexton is a vastly experienced number 10 and has helped Leinster to win four European Champions Cups since making his debut 12 years ago.
The 33-year-old is also the province's all-time leading points scorer and head coach Leo Cullen feels he is the perfect candidate to take over the leadership role.
Cullen told the club's official website: "Johnny is a player and person who is always striving to improve and get better and he has driven incredibly high standards during his time at Leinster.
"He has become one of the most decorated players in the game."