Payne, 31, who found fame on The X Factor with the boy band, died after falling from a balcony on the third floor of a hotel in Buenos Aires, Argentina.
A statement signed by Harry Styles, Zayn Malik, Louis Tomlinson and Niall Horan said: “We’re completely devastated by the news of Liam’s passing.
“In time, and when everyone is able to, there will be more to say.
“But for now, we will take some time to grieve and process the loss of our brother, who we loved dearly.
“The memories we shared with him will be treasured forever.
“For now, our thoughts are with his family, his friends, and the fans who loved him alongside us.
“We will miss him terribly. We love you Liam.”