Your code as posted does not compile:

$ perl -cw 11135816.pl 
No such class list at 11135816.pl line 6, near "my list"
syntax error at 11135816.pl line 6, near "my list ="
syntax error at 11135816.pl line 9, near "$1
print"
Global symbol "$the_rest" requires explicit package name at 11135816.p
+l line 10.
Bareword "list" not allowed while "strict subs" in use at 11135816.pl 
+line 6.
11135816.pl had compilation errors.
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Cleaning it up and fixing the regex by anchoring to the end and allowing spaces in the first group we have:

use strict;
use warnings;

my $list = "This is my list";
$list =~ /(.+)\s(\w+)$/;
my $last     = $2;
my $the_rest = $1;
print $the_rest . "\n";    # "This is my"
print $last . "\n";        # "list";
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