The Brit Award winner and three-time Mercury Music Prize nominee tops the bill at the 13th annual festival at Glanusk Park, Powys, on 20 August.
Fellow UK acts Belle and Sebastian, on Thursday, James Blake, on Friday, and Wild Beasts, on Sunday, have already been named as the other headliners.
The festival was a sellout last year, with about 20,000 people attending.
Festival director Fiona Stewart said: "Laura returns for her third performance at Green Man, her legendary performances have always gone down a storm and we're already feeling awestruck imagining her Saturday night set, full of new album material."
Other new acts booked for this year's Green Man festival include Charlotte Church's Late Night Pop Dungeon - "a karaoke experience unlike any other you've experienced before, or ever will again", re-formed 1990s alt-rockers Lush, and DJ Pete Paphides.
Among the other prominent acts appearing are Grandaddy, Tindersticks, White Denim, Fat White Family, Cate Le Bon, Gun Outfit, and The Membranes.
Previous headliners have included legendary Belfast-born blues and rock singer Van Morrison, ex-Led Zeppelin frontman Robert Plant, US singer-songwriter Patti Smith, Cardiff rockers Super Furry Animals, Fleet Foxes, Jarvis Cocker and Doves.
Founded in 2003, Green Man has become one of the most popular alternative festivals.
It won the 2010 best medium-sized event and 2012 best "grass roots" event at the UK Festival Awards, and 2015 best festival at the Live Music Business awards.
Alt-folk singer-songwriter Laura Marling has been unveiled as a headline act for the 2016 Green Man festival.