The solutions provided seem very complex. Here's something simpler:

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

for (;;) {
   my $head = <>;
   my $body = <>;
   last if !defined($body);

   chomp( my $seq = $body );
   my $len = length($seq);
   $head =~ s/(length=)\d+/$1$len/;

   print($head, $body);
}
[download]

Update: Length was off by one because of lack of chomping. Fixed. Thanks graff.