H1 approved but waiting on H4 for spouse

Hello community members: I need your suggestions/experience on an issue I am currently facing. I am on J1 and my wife is on J2 VISA. Recently I have accepted a position and they have filed for my H1B which is approved (premium processing). At the same time, we also applied to my wife’s H4 VISA (I-539). While my H1B is approved and I need to join the second week of January, it appears that my wife will not have an approved I-539 (change of status from J2 to H4). Do I need to wait for her I-539 to get approved before I join my position or as long as my H1B is approved and her application is filed we are ok? Thank you for your input.

You do not have to wait for her approval. You can join on H1B. She will be in something called as Period of authorized stay. She can legally stay in the US and has no direct impact to you.