The simplest modification to your code as it stands would be using capturing parentheses (see Extracting matches and Backreferences in perlretut) to grab your tildes for your substitutions. I will also add the g modifer (see Modifiers in perlre) so you can replace all groups of tildes in one pass. Your code might then look like:

sub add_line_break
{
my (@out)=@_;
for (@out) {
     s/(~+)/$1\n/g;
 }
return wantarray ? @out :$out[0];
}
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A logical change I would make (and a slight efficiency boost) would be to change that to a substitution applied to a location preceded by a tilde but not followed by a tilde:

s/(?<=~)(?!~)/\n/g;

That uses a positive look-behind and a negative look-ahead (see Looking ahead and looking behind in perlretut).

As a side note, when you want to understand what a regular expression does, check out YAPE::Regex::Explain. It can be very useful when learning regular expressions and when dealing with unfamiliar/old code.