my final code:

#!/usr/bin/perl 

use strict;
use warnings;
use diagnostics;


# Open file1 to read
open my $input_file1, '<', "rmsd1.xvg" or die qq{Failed to open "rmsd1.xvg" for writing: $!};

# Open file2 to read
open my $input_file2, '<', "rmsd2.xvg" or die qq{Failed to open "rmsd2.xvg" for writing: $!};

# Open new file to write
open my $out_file, '>', "rmsd.xvg" or die qq{Failed to open "rmsd.xvg" for writing: $!};

# Copy data from one file to another.

my %file2data;
while(<$input_file2>)
{ 
 next if /(^\s*$)|(^#)|(^@)/;
 my @columns2 = split;
 $file2data{$columns2[0]} = $columns2[1];
}

while(<$input_file1>)
{ 
 next if /(^\s*$)|(^#)|(^@)/;
 my @columns1 = split;
 print $out_file join("\t", $columns1[0],$columns1[1], $file2data{$columns1[0]}), "\n";
}
close($input_file2);
close($input_file1);
close($out_file);