Why were Gimli, Legolas, and Boromir chosen?

[Niere-Teleliniel]

Boromir was prolly chosen because of the dream that sent him to Rivendell in the first place.

Seek for the sword that was broken:
In Imladris it dwells;
There shall be councils taken
Stronger than Morgul-spells.
There shall be shown a token
That Doom is near at hand,
For Isildur's Bane shall waken,
And the halfling forth shall stand.
-FOTR, pg 323

I think Elrond and the council saw this as fate choosing a companion for the Fellowship.