The 25-year-old, who scored 18 goals across 69 appearances for the Spanish club, will officially join the Seagulls on June 8.
Hughton is glad to have got the transfer done and dusted early in the window, with reports suggesting that the transfer is worth a little over £5m.
"We are delighted that Florin has agreed to join us. He is a player that we have tracked for some time, and he will add a new dimension to our attacking options," he told the club's official website.
"He is a very hard-working player, and has proven his quality at the highest level in Spain, as well as at international level. I am looking forward to working with him next season."
Andone arrived at Deportivo in July 2016 on the back of a campaign that saw him net 27 times in 58 games for Cordoba.