MySQL server migration to new hardware I have to migrate working DB from old server (~50 Gb, mysql-5.5.43, openvz, all data in InnoDB) to a new hardware and new mysql version (mysql-5.6.28, debian). DB is "alone" - no replica servers. Dumps regulary made by mysqldump. Also software on PHP is running on server

Simple move using mysqldump isn't ok, 'cause restoring base is longs about 8 hours. I have no window of time for this...

So, there's a thought: make new server as a slave to existing server, wait till mysql replication sync is done,  turn off old server, make slave become master and continue working. Is this possible? Will be there any software-kind problems?

Or, this thought is wrong. If so, how, then, I have to migrate my DB to new hardware and software with minimal downtime?
In your case restoring database is taking more time, so I suggest to use AWS database migration service. 

It's very simple,less human work and fastest method. And also your real time data will sync.
Instead of replication use this.