Tour captain Sam Warburton skippered the Lions in the first two Tests against Australia in 2013 before injury ruled him out of the decisive third match.
And the Wales flanker, who has carried a knee injury into the tour, must make do with a place among the substitutes against New Zealand at Auckland's Eden Park.
In his absence, Ireland's O'Mahony has secured the prestigious honour of leading the tourists versus the reigning world champions.
Farrell had been in doubt due to a quadriceps injury, while Sexton impressed at fly-half in a decisive 32-10 victory over the Maori All Blacks last weekend, but it is the England man who has won the race for the coveted number 10 shirt.
Introducing the Lions captain for the first Test...
Congratulations, Lion #832 Peter O'Mahony!
— British&Irish Lions (@lionsofficial) June 21, 2017
There were a number of surprises in Warren Gatland's XV, with Alun Wyn Jones in for Maro Itoje at lock and Liam Williams keeping full-back Leigh Halfpenny out of the side.
Elliot Daly, who shone on the wing against the Chiefs on Tuesday, has been favoured over George North, a star of the 2013 series triumph over the Wallabies.
The Lions go into the first Test on the back of four wins and two defeats from six tour games, Blues and Highlanders having bloodied the nose of the visitors, who have only won a series in New Zealand once, in 1971.
Lions XV: Williams, Watson, Davies, Te'o, Daly, Farrell, Murray; Vunipola, George, Furlong, Wyn Jones, Kruis, O'Mahony, O'Brien, Faletau.
Replacements: Owens, McGrath, Sinckler, Itoje, Warburton, Webb, Sexton, Halfpenny.
Photo by Getty Images: Peter O'Mahony of the British and Irish Lions