Hello razmeth, and welcome to the Monastery!

The IO::Tee module recommended by BrowserUk is likely the best fit for your stated requirements. But if you need something fancier, consider Tie::STDOUT:

#! perl
use strict;
use warnings;

my $file = 'test.txt';

open(my $fh, '>', $file)
    or die "Cannot open file '$file' for writing: $!";

use Tie::STDOUT
    print  => sub
    {
        print  @_;
        print  $fh '[', scalar localtime, ']: ', @_;
    },
    printf => sub
    {
        printf @_;
        print  $fh '[', scalar localtime, ']: ';
        printf $fh @_;
    };

print  "Perl is cool!\n";
printf "Pi is %f\n", atan2(1, 1) * 4;

close $fh
    or die "Cannot close file '$file': $!";
[download]

Output:

16:32 >perl 1504_SoPW.pl
Perl is cool!
Pi is 3.141593

16:32 >
[download]

Contents of file “test.txt”:

[Tue Jan  5 16:32:03 2016]: Perl is cool!
[Tue Jan  5 16:32:03 2016]: Pi is 3.141593
[download]

Hope that helps,