class_vars was being called too late to be of any use.

Putting a BEGIN block around a sub definition is useless, as a sub definition doesn't generate code to execute.

Contrary to what you said, you weren't getting a syntax error, you were getting a strict error. Quite appropriate since you asked for it.

Solution:

BEGIN {
   package class_vars;

   use strict;
   use warnings;

   sub import {
      shift;
      my $pkg = caller;
      for my $var (@_) {
         eval("
            package $pkg;
            use vars '\$$var';
            sub $var {
               \$$var = \$_[1] if \@_ > 1;
               return \$$var;
            }
         ");
      }
   }

   $INC{'class_vars.pm'} = __FILE__;
}


{
   package MyPackage;

   use strict;
   use warnings;

   use class_vars qw( one two three );

   sub init_one_from_three {
      $one=$three-2;
   }

   sub new {
      my $package=shift;
      my $parms=$_[0];
      
      my $this={};

      foreach(keys %$parms) {
         no strict 'refs';
         $$_=$parms->{$_};
      }

      bless $this, $package;
   }
}


{
   use strict;
   use warnings;

   my $p=new MyPackage({three => 3,});

   $p->two(2);
   $p->init_one_from_three;

   printf "one=%d two=%d, three=%d\n", $p->one, $p->two, $p->three;
}
[download]

one=1 two=2, three=3
[download]

BEGIN {
   ...
   $INC{'class_vars.pm'} = __FILE__;
}
[download]

Package declarations are lexically scoped. You had lots of needless package switching.

I left in the limit that class vars must be scalars.

You call them class vars, but then you initialise them when constructing an instance, and you access them via a class instance. They're not class variables at all. They're object attributes, and you're going the wrong way about creating a singleton.

Update: Adjust the value in %INC as per reply.