Regular expression "replace string interpolation" problem

[cLive ;-)]

For tidiness, I want to store a bunch of regular expressions outside of a script, but I can't work out how to get interpolation of the replace string correct. Here's a simple example:

#!/usr/bin/perl
use strict;
use warnings;

# works as expected
my $text = 'Hello world';
$text=~ s/(\w+)/$1 Perl/;
print "Regular regex: $text\n";

# but now try with variable interpolation
my $text2 = 'Hello world';
my $match = qr/(\w+)/;
my $replace = '$1 Perl';

$text2 =~ s/$match/$replace/e;

# not what I want
print "Interpolated regex: $text2\n";

I won't bore you with all the variations I've tried so far, but I've been playing with this for an hour (including qr and different modifiers) and it's driving me crazy. Any ideas?