kindred soul; congenial friend
A somewhat literary or formal expression for a close friend with whom one shares a deep mutual understanding.
彼は私にとって会心の友だ。
He is a kindred soul to me.
会心の友と呼べる人はそう多くない。
There aren't many people you can call a congenial friend.
心の友 is similar in meaning but more common and slightly less formal; 会心の友 carries a nuance of mutual understanding and shared feelings.
Formed from 会心 in the sense “satisfying or congenial to one’s heart” and 友 “friend,” denoting a deeply congenial friend.