The intent of the screenwriters could be for Legolas to replace Elrond's sons (Elladan and Elrohir), which do not appear in any of the six middle earth movies.
So, Legolas could end up living at Rivendell and helping Aragorn in his first adventures, and maybe even acting as a liaison between Rivendell, Mirkwood (quickly visiting his former home from time to time) and Lothlorien.
This long-term friendship could also explain Legolas' behavior at the council of Elrond ("This is no mere Ranger. He is Aragorn, son of Arathorn. You owe him your allegiance."), when Boromir quickly dismisses Aragorn as an ignorant ranger.
The extended edition of the Battle of the Five Armies, especially the screenwriters commentary, will hopefully have a definitive answer.