ALTER TABLE ..
can be used to move tables from one database to another :
alter table my_old_db.mytable rename my_new_db.mytable
Warning : as you asked, this is a move, not a copy to the new database!
But you will keep table data (and not integrity constraints if they apply in your case)
Regarding php, php is able to run sql commands so it won't be a problem (i can be more precise if you wish).