Another Video released over #AskGoogleWebmasterby John Mueller describing the changes when a server migration is done.

He said that the only thing that changes temporarily when you move a site from one server to another is how fast google bot crawls the content. Google will check back to test how fast its crawler can crawl your site without impacting the server in a negative way. Check out the video for more:

In short, assuming nothing else changes with the server move. The only change will be that Google slows its crawl to begin testing how fast it can crawl your site within taking the server down because of overloading it. Outside of that, you should be fine.

Also Read>> Google: John Mueller Describes Where to Insert JSON-LD Data

It is assuming that nothing gets changed except the serer move and Google slows its crawl rate to crawl.