Alitalia president Roberto Colaninno and chief executive Gabriele Del Torchio have been charged "to continue negotiations for the drafting of a definitive agreement with the UAE company," said a statement from the board.
Italian transport minister Maurizio Lupi, who has been deeply involved in the case, welcomed the announcement on Twitter.
"The board of directors of Alitalia gives a mandate to close (negotiations) with Etihad. Good! Italy is again attracting foreign capital. Now forward, swiftly!" he tweeted.
Etihad has for months been negotiating to buy up to 49 percent of the stricken Italian flag carrier, which is facing bankruptcy.
But talks have stumbled over Alitalia's heavy debt load and predicted job cuts of between 2,400 and 2,500 Ethiad wants as part of the deal.
According to Italian media, the issue of debt had still not been discussed after a meeting between the banks and the Italian government on Thursday.
Unions are expected to meet on 12th June.
Senior officials from the northern Italian region of Lombardy have also expressed concern this week about the fate of Milan's Malpensa airport, which they fear could be seriously penalised in the Etihad's projects.