"We will be leaving tomorrow afternoon, God willing," Mahdi al-Mushat, a representative of the Houthi movement, wrote on his Facebook page on Tuesday.
"We confirm that we will leave for Kuwait, carrying all the worries, wounds, aspirations and hopes of the great Yemeni people," Yahya Duwaid, a representative of the ex-president Ali Abdullah Saleh, wrote on his account, Reuters reported.
Envoys from Yemen's Houthi movement and Saleh's party had refused to talk peace amid ongoing ground combat and airstrikes by a Saudi-led military coalition which they say violated a truce agreed a week before.
But concerted pressure from regional and international diplomats has succeeded in bringing the factions to the table with their enemies from Yemen's former fugitive government which they ousted from the capital in March of last year.