The boy band were among a host of acts added to the bill yesterday, including Katy Perry, Kings of Leon, Ed Sheeran and Bastille.
They join the likes of Pharrell Williams, Rita Ora and Paolo Nutini during the weekend-long festival to be attended by up to 50,000 revellers in Glasgow Green on Saturday May 24 and Sunday May 25.
Last week, Coldplay were named as the headline act for the first day of the festival with One Direction, Bastille, Pharrell, Jake Bugg, Lily Allen and Ed Sheeran also performing on the Saturday.
One Direction said: "We're so excited to perform at Radio 1's Big Weekend in Glasgow. Glasgow, we are coming to get you. We're going to put on a great show and we can't wait to see you all there."
Kings of Leon, The Vamps, John Newman, Ora, The 1975, Tinie Tempah and Nutini will all perform on the Sunday with Perry closing the festival.
Kings of Leon drummer Nathan Followill said: "We've heard great things, and we can't wait to experience them first-hand."
The event is part of the BBC's contribution to the Glasgow 2014 Commonwealth Games.
Radio 1 controller Ben Cooper said: "It's a phenomenal line-up, probably the best in the world this year, in one of the world's great music cities."
In the lead-up to the Big Weekend, some of the biggest names in music, comedy and business are to pass on tips to youngsters as part of the festival.
Emeli Sande, Kevin Bridges and Sir Richard Branson will be among a host of famous people to hold practical workshops, question and answer sessions and masterclasses as part of the Radio 1 Academy in Glasgow between May 10 and 16.
On Saturday May 17, Radio 1Xtra is hosting an outdoor gig featuring urban music at the Riverside Museum in Glasgow, and on the night before the Big Weekend begins, a live DJ event for 14,000 people will be held in the city's George Square featuring Annie Mac, Pete Tong, Zane Lowe and Danny Howard.