Or 'Congratulations on moving, XXX'?

没有固定的说法。根据下列链接中的3和4，似乎可以这样：

Congratulations on/for moving to your new premises.
Congratulations to XXX on/for moving to your new premises.

https://career-management-promotions.knoji.com/congratulatio...


1. Congratulations! Your new office place is really a wonderful place to work on. The ambiance is so cool that will surely make your employees perform their tasks well.

2. Cheers for your new office! I wish that your new office place is going to be a source of prosperity. God bless!

3. Congratulations on the opening of your new office. I heard that this one is a wider and greater place to work on. God bless and I pray that you may have more income and may the presence of prosperity will be there always. Congratulations!

4. Wow! My million greetings of congratulations for opening your new office. I wish for never ending success as you start running your business in your new office. All the best for you and cheers!!

5. Wow! I heard the good news and it really make me stun to know that you have just opened a new office. My warmest greeting of congratulations and I wish that as you start your business in your new office, only best luck and success will fill in your new place of work.

6. Be able to have your own new office is a sign of your success and just a preparation for a bigger challenge when it comes to running your business. Well! Congratulations! And I believe in your talent that you will be able to make your start shining in its brightest spark.

7. Wow! Congratulations for opening your new office. This is a proof that you are ready now to take the next steps of your ladder in success. Enjoy your new challenging chapter of your business. And I know that in you as a business man/woman you can really make it on top!

8. Starting up to build a new office is really uneasy task but, because of your self-discipline and self-dedication in years of your service, you have now successfully opened a new office for more business success. Congratulations! Keep up the good work!

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Note added at 38 mins (2018-03-11 07:14:21 GMT)
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If you search "Congratulations Messages for New Office“, you will see a lot of images of the cards for this purpose. One of them says ”Congratulations on your new office“. You can modify it into "Congrats on your new premises“

乔迁新居贺词:乔迁之喜贺词_乔迁新居贺词_教育_太平洋亲子网
edu.pcbaby.com.cn › 早教资源 › 短信贺词大全 › 乔迁新居贺词
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Jul 4, 2014 - 乔迁之喜贺词. Best wishes for your new home. 良禽择木、乔木莺声、莺迁吐吉、德必有邻. To choose a master to serve., arbor voice, warblers, Germany will have moved out, O. 高第莺迁、莺迁乔木、新居落成、乔迁志庆. The warbler warbler moved, moved trees, new home, housewarming celebration. 乔迁贺喜.
乔迁之喜in English - What is the meaning of 乔迁之喜- Translation ...
approachinese.com/dict/zh2en/乔迁之喜/
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乔迁之喜 Add to My Vocabulary. PinYin qiáo qiān zhī xǐ Simplified 乔迁之喜 Traditional 喬遷之喜. congratulations on house-moving or promotion (idiom); Best wishes for your new home!

OR
Congratulations on the joyful occasion of AA company’s (or your) relocation!