这样写对吗:Let us welcome Mr. Gary Li, a new member join BJ Office as a Manager on June 8?

1)Better to use "Let's" than "Let us". to show suggestion but not asking for permission.
2)better to say "a new member to join" .....
In this sentence there is already a finite verb, so just a Non-Finite Verbs is needed.

Attention everybady, let us welcome Mr.Gary, a new manager in BJ office.

如果是口语，就对的。不用说的那么严谨。

Let's welcome Mr Li, a new manager joined/to join in our BJ office on June 8th
看你说这句话的时候是6月8日之前还是之后，然后决定用过去时还是将来时。

用祁使句吧!let us 3掉 不过 join还有个用法join in这里不用加in.大概就是这样吧!