it's really strange but I feel as if I have known you (him/her) for a long time
It's weird but even though we have only just met, I feel a closeness as if we have known each other for a really long time
「不思議だけど」＝ it's really strange but... / it's weird but... / it's mysterious but...
「昔から知ってる様な親近感や安心感を感じる」＝ I feel as if I have known you (him/her) for a long time / I feel a closeness as if we have known each other for a long time
伝えたい事を伝えるためにこちらの文章が良いと思います：
It's weird but even though we have only just met, I feel a closeness as if we have known each other for a really long time
I feel like I’ve known you for such a long time, although we just met, because I feel really close and I feel like I can trust you.
really close は親近感を凄く持てると言う意味として使います。
I feel like I’ve known you for such a long timeは昔からの知り合い見たいと言う例えです。この例えはこういう場合によく使われます。
I feel like I can trust you は信用できるあるいは安心感を持てると言う意味です。
お役に立ちましたか？^_^
イギリス 
アメリカ合衆国 
