The problem is finding something to terminate your input that will not legitimately occur in that input. You can use BrowserUk's suggestion of ^Z/^D in an endless version of your while loop, breaking out with a test for eof.

use strict;
use warnings;

my $prompt = q{Add input (CTRL-D to finish) : };
my @input = ();
print $prompt;

while( 1 )
{
    last if eof STDIN;
    push @input, scalar <STDIN>;
    print $prompt;
}
print qq{\n};

chomp @input;
print
   qq{Your input:\n},
   do { local $" = qq{\n  -->}; qq{  -->@input}; },
   qq{\n};
[download]

Running it (the terminating ^D does not show up)

knoppix@Knoppix:~/perl/Monks$ ./spw796843
Add input (CTRL-D to finish) : This is
Add input (CTRL-D to finish) : a few words
Add input (CTRL-D to finish) : of nonsense
Add input (CTRL-D to finish) : 
Add input (CTRL-D to finish) : including a
Add input (CTRL-D to finish) : blank line
Add input (CTRL-D to finish) : 
Your input:
  -->This is
  -->a few words
  -->of nonsense
  -->
  -->including a
  -->blank line
knoppix@Knoppix:~/perl/Monks$
[download]

I usually tidy up the last prompt and the ^D (which, IIRC, does appear on Solaris) with the following change to the code.

use strict;
use warnings;

my $prompt = q{Add input (CTRL-D to finish) : };
my $maskPrompt
   = qq{\r}
   . ( q{ } x ( length( $prompt ) + 2 ) )
   . qq{\r};
my @input = ();
print $prompt;

while( 1 )
{
    last if eof STDIN;
    push @input, scalar <STDIN>;
    print $prompt;
}
print $maskPrompt;

chomp @input;
print
   qq{Your input:\n},
   do { local $" = qq{\n  -->}; qq{  -->@input}; },
   qq{\n};
[download]

I hope this is of interest.