One query two MySQL servers I have two MySQL servers on different server computers. Is it possible to execute single query like this:

INSERT INTO database1.xxxxx SELECT table1.field1, table2.field1 FROM database2.xxxxx INNER JOIN ....

EDIT: I will make cron job witch will run this once a day. I don't need synchronization.
First of all in this scenario you have two remote MySQL server you need to have two connections.
MySQL does not support such a query wherein it connects to other server and get details, in my understanding no other RDBMS does this kind of thing.

INSERT [LOW_PRIORITY | HIGH_PRIORITY] [IGNORE]
    [INTO] tbl_name [(col_name,...)]
    SELECT ...
    [ ON DUPLICATE KEY UPDATE col_name=expr, ... ]


Conclusion:
NO. You can't write such query on Two Mysql servers.