Note to Sivan:  I'm using Quenya; just because I like it.  Thanks to The Grey Company for the translations

After everyone had eaten their fill, they then went to the Hall of
Fire. The four friends were walking together, with Elrond and
Thranduil walking behind. The two elf-lords smiled as they listened
to the laughter as Estel wound up a rather lengthy, albeit somewhat
implausible story about Legolas stalking a large wild animal through
the woods of Mirkwood. Estel finished, saying, "Would you believe it
turned out to be a rabbit?"
Legolas, with what dignity he had, replied, "Well, it was a very
huge rabbit." With that, he swept into the Hall of Fire, leaving his
companions outside.
Estel caught up with his friend, and said with a smile, "It
certainly was large." Legolas glared at him, then started to laugh
as well. They waited until the twins had joined them, and all four
sat together to listen to the songs and tales that would be sung and
told that evening.
Thranduil and Elrond came to the center of the hall. "Vedui' il'er.
The singing will start shortly. However, King Thranduil and I would
like to take just a few minutes of your time. Lle auta yesti',
Thranduil."
King Thranduil joined Elrond. "Ta naa amin saesa. Legolas
Thranduilion; Aragorn, son of Arathorn; Elladan Elrondion; and
Elrohir Elrondion, please come forward."
The four named looked at each other, then moved in front of their
fathers. Elrond smiled at them. "Don't worry, you have done nothing
wrong. We have something we wish to say to all of you."
Thranduil nodded at Elrond's words. "It has been my pleasure to
welcome the sons of Elrond to Mirkwood many times. Therefore,
tonight, with Elrond's permission, I would like to welcome Elladan
and Elrohir into the house of Thranduil. You have been a friend of
my son's and I wish that, for the rest of your lives, you would
always be in my heart as sons of Thranduil. Please accept these
gifts as a token of my esteem." With that, he presented each of the
twins with a small mithril-bound box. Upon opening them, they saw a
brooch, with the crest of Mirkwood entwined with the crest of
Elrond. "Wear them in good health," said Thranduil.
The eyes of Elladan and Elrohir were both bright with unshed tears,
and they bowed their heads with a whispered "Diola lle, Ada."
Both Elrond and Thranduil smiled and replied, "Lle creoso."
The king then turned to Estel. "Estel, I have something special for
you. I have seen the friendship between you and Legolas grow into a
bond that nothing will ever break. That bond is one of brothers.
Greater love has no one but that he will give his life for his
brother. Many times I have seen both of you return, injured, with
your only concern being the other should be treated before yourself.
I have envied this love, and now I wish to honor it. Aragorn, son of
Arathorn, I name you as brother to Legolas Thranduil, with all its
privileges. I will always keep you in my heart as a son. I believe
Lord Elrond has something he wishes to say." With that, Thranduil
stepped back.
Elrond smiled at Estel and Legolas. "I, too, have seen the
friendship and brotherly love develop between the two of you.
Legolas Thranduilion, I hereby welcome you as brother to Estel,
Elladan, and Elrohir with all its privileges. I, too, will always
keep you in my heart as my son. You will always be welcome to the
house of Elrond."
The two Lords then beckoned Estel and Legolas to come nearer. Two
boxes of gold bound with silver were presented to the two. The two
friends opened them. Inside, nestled on a swath of blue silk, were
rings made of mithril, with the crest of Mirkwood and Rivendell
entwined. "Welcome, my sons. May your friendship ever endure."
Both Legolas and Estel had tears in their eyes. Finally, when he
could trust his voice not to betray his emotions, Estel hugged both
Elrond and Thranduil, and said, " Amin harmuva onalle e'coramin.
Diola lle." Legolas could only smile through his tears, and say,
huskily, "Diola lle." Both fathers were also trying, without much
success, to control their own emotions. "Lle creoso, ion nin."
With that, the nights' entertainment began.

Translations
Vedui' il'er: Greetings everyone
Le auta yesti': You go first
Ta naa amin saesa: It is my pleasure
Amin harmuva onalle e'coramin: I shall treasure your gift in my heart
Diola lle: Thank you
Lle creoso: You're welcome