Here you go, adapted from this pythong example

package main;

my ($app) = MyApp->new();
$app->MainLoop();

package MyApp;

use base qw(Wx::App);

sub OnInit {

    my ($self)  = shift;
    my ($frame) = MyFrame->new;

    $frame->Show(1);
    $self->SetTopWindow($frame);

    return 1;
}

package MyFrame;
use Wx::Perl::Carp;
use Wx;
use base 'Wx::Frame';

sub new {
    my $class = shift;
    my $self  = $class->SUPER::new( undef, -1, 'Hiya there' );

    my $panel = Wx::Panel->new( $self, -1 );

    use Wx qw' wxLB_SINGLE ';
    $self->{lb1} = Wx::ListBox->new(
        $panel, -1,
        [ 10,  10 ],
        [ 100, 200 ],
        [ "red", "green", "blue", 1 .. 8 ], wxLB_SINGLE
    );

    use Wx::Event qw( EVT_LISTBOX );
    EVT_LISTBOX( $self, $self->{lb1}, \&on_select );

    $self->{lb2} = Wx::ListBox->new(
        $panel, -1,
        [ 120, 10 ],
        [ 100, 200 ],
        [ "10", "20", "30" ], wxLB_SINGLE
    );

    use Wx qw' wxTE_READONLY wxTE_MULTILINE  wxDefaultPosition  wxDefa
+ultSize ';

    $self->{logtext} = Wx::TextCtrl->new(
        $self, -1, "Welcome to wxPerl\n",
        wxDefaultPosition,
        [ 200, 100 ],
        wxTE_READONLY | wxTE_MULTILINE
    );

    Wx::Log::SetActiveTarget( Wx::LogTextCtrl->new( $self->{logtext} )
+ );

    use Wx qw' wxVERTICAL  wxEXPAND wxHORIZONTAL wxALL ';
    my ($topsizer) = Wx::BoxSizer->new(wxVERTICAL);
    my ($logsizer) = Wx::BoxSizer->new(wxHORIZONTAL);

    $topsizer->Add( $panel, 0, wxEXPAND );
    $topsizer->AddSpacer(1);
    $logsizer->Add( $self->{logtext}, 1, wxALL | wxEXPAND, 0 );
    $topsizer->Add( $logsizer, 1, wxEXPAND );

    $self->SetSizer($topsizer);
    $self->Layout();
    $topsizer->Fit($self);
    $topsizer->SetSizeHints($self);

    $self->{target} = MyTextTarget->new( $self->{lb2} );

    return $self;
}

sub on_select {
    my ( $self, $event ) = @_;
    my $selection = $self->{lb1}->GetSelection();

    my $text = $self->{lb1}->GetStringSelection();
    carp( 'selected text ', $text );
    my $text_obj = Wx::TextDataObject->new($text);

    my $source = Wx::DropSource->new( $self->{lb1} );
    $source->SetData($text_obj);

    use Wx qw' wxDrag_AllowMove wxDrag_DefaultMove wxDragMove wxDragCo
+py
      wxDragMove
      wxDragLink
      wxDragCancel
      wxDragNone

      ';

    my $drop_result = $source->DoDragDrop(wxDrag_DefaultMove);

    carp(
        'drop_result(',
        $drop_result,
        ') ',
        'wxDragCopy (',
        wxDragCopy,
        ') ',
        'wxDragMove (',
        wxDragMove,
        ') ',
        'wxDragLink (',
        wxDragLink,
        ') ',
        'wxDragCancel (',
        wxDragCancel,
        ') ',
        'wxDragNone (',
        wxDragNone,
        ') '
    );

    if ( $drop_result == wxDragMove ) {    #the selection was moved-no
+t copied
        carp( 'deleting  ', $self->{lb1}->Delete($selection) );
    }
}

package MyTextTarget;
use Wx::Perl::Carp;
use Wx::DND;
use strict;
use base qw( Wx::TextDropTarget );

sub new {
    my $class         = shift;
    my $target_widget = shift;
    my $self          = $class->SUPER::new(@_);
    $self->{target_widget} = $target_widget;
    $self->{target_widget}->SetDropTarget($self);

    $self->{text_obj} = Wx::TextDataObject->new($target_widget);
    $self->SetDataObject( $self->{text_obj} );

    return $self;
}

sub OnDropText {
    carp("OnDropText @_ ");
    my ( $self, $x, $y, $d ) = @_;
    $self->GetData();
    my $text = $self->{text_obj}->GetText();
    my $c    = $self->{target_widget}->GetCount();
    carp( 'count ', $c );
    $self->{target_widget}->InsertItems( [$text], $c );

    return 1;    # important
}

__END__
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