英语问题He will let you know as soon as he arrives in Beijing ne

as soon as 意为 一什么就什么 ,as soon as引导的条件状语从句,He will let you know.是主句he arrives in Beijing next week 是,从句.条件状语从句主句用一般将来时,从句用一般现在时,即常说的主将从现.既然用一般现在时,he 为第三人称,当然是arrives了.
如果后面从句主语是I We they 等非单三人称,从句谓语不变单三形式,因为不是单三人称.
如果是从句主语是 She He It 等情况,才用变单三形式,来体现第三人称单数.

后面的arrives实际上是因为时间状语从句要用一般现在时表示将来，而不是你所说的情况。