Disclaimer: I find the design questionable... you should consider not using constant (in fact Conway's Perl Best Practices recommends against it, e.g. Perl::Critic::Policy::ValuesAndExpressions::ProhibitConstantPragma) and look at alternatives such as using a locked hash (or even a function) to return your "constant" values.

As is said, Perl gives you just enough rope to hang yourself with, so here you go:

package ConstExporter;
use warnings;
use strict;

my %CONSTANTS = (
    foo => "abc",
    bar => "xyz",
    quz => "123",
);

sub import {
    my ($class, @export) = @_;
    my ($callpack) = caller;
    for my $exp (@export) {
        die "bad constant name '$exp'"
            unless exists $CONSTANTS{$exp};
        no strict 'refs';
        *{"${callpack}::$exp"} = sub () { $CONSTANTS{$exp} };
    }
}

1;
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Use it in the usual way: use ConstExporter qw/foo bar/;