You really need to use strict (use strict;). Consider what happens when the following line invokes the die.

open my $wave,    '>', 'Wave' or die "Can't open $wave: $!";
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Using three parameter open and error handling is laudatory, but omitting strict and a few other areas of your code could use some TLC. Consider the following light do over:

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

open my $wave,        '>', 'Wave'        or die "Can't open 'Wave': $!
+";
open my $keywords,    '<', 'Agents'      or die "Can't open 'Agents': 
+$!";
open my $search_file, '<', 'Definitions' or die "Can't open 'Definitio
+ns': $!";

my $keyword_or = join '|', map {chomp; qr/\Q$_\E/} <$keywords>;
my $regex      = qr|\b($keyword_or)\b|;

while (defined (my $line = <$search_file>)) {
    while ($line =~ /$regex/g) {
        next if $line =~ /(SCRIPTNAME|DESCRIPTION)/;
        print $wave $line;
        last;
    }
}
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Things to note:

• use of strict
• error handling mentions the file name rather than the file function
• Avoid using $_ where a manifest variable can be used instead (c.f. $line)
• use a statement modifier if to skip in the inner loop to make logic flow clearer
• terminate inner loop once the line has been printed to avoid multiple copies
• remove the explicit file close statement. With lexical file handles the files are closed when the handle variable goes out of scope so it unusual to need to explicitly close files