You could just put it in package main, as in $main::db = new DB();, although it's one of those design choices that can get very deeply sedimented in a large project, and hard to change later.

If you're feeling amibitious, why not try a singleton class, with a class method that returns the data you need?

package GlobalVarsSingleton;
my $instance;

# a 'private' ctor
sub _new { 
 # init stuff
}

sub Instance {
   my ($class, %args) = @_;
   unless (defined $instance) {
     $instance = $class->_new(%args);
     return $instance;
   } else {
     return $instance;
   }
 }
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The singleton ensures that you'll only have one instance of the data per interpreter, and the calling code doesn't have to care where that data lives.