FileControl.Xaml

<UserControl x:Class="Namespace.FileControl"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" 
             xmlns:d="http://schemas.microsoft.com/expression/blend/2008" 
             mc:Ignorable="d">
    <Grid Height="Auto">
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="Auto"/>
            <ColumnDefinition/>
            <ColumnDefinition Width="25"/>
        </Grid.ColumnDefinitions>
        <Label x:Name="Label" Grid.Column="0"/>
        <TextBox x:Name="PathTb" Grid.Column="1" TextChanged="PathTb_OnTextChanged"/>
        <Button Grid.Column="2" Content="..." ToolTip="Browse for file" Click="BrowseClick"/>
    </Grid>
</UserControl>

FileControl.xaml.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using Microsoft.Win32;

namespace Namespace
{
    /// <summary>
    /// Interaction logic for FileControl.xaml
    /// </summary>
    public partial class FileControl : UserControl
    {
        public FileControl()
        {
            InitializeComponent();
        }

        public static readonly DependencyProperty FilterProperty = 
            DependencyProperty.Register("Filter", typeof(string), typeof(FileControl), new PropertyMetadata(default(string)));
        public string Filter
        {
            get { return (string)GetValue(FilterProperty); }
            set { SetValue(FilterProperty, value); }
        }

        public static readonly DependencyProperty LabelTextProperty = 
            DependencyProperty.Register("LabelText", typeof(string), typeof(FileControl), new PropertyMetadata(default(string), (o, e) => ((FileControl)o).Label.Content = e.NewValue));
        public string LabelText
        {
            get { return (string)GetValue(LabelTextProperty); }
            set { SetValue(LabelTextProperty, value); }
        }

        public static readonly DependencyProperty PathProperty = 
            DependencyProperty.Register("Path", typeof (string), typeof (FileControl), new PropertyMetadata(default(string), (o, e) => ((FileControl)o).PathTb.Text = (string) e.NewValue));

        public string Path
        {
            get { return (string) GetValue(PathProperty); }
            set
            {
                SetValue(PathProperty, value);
            }
        }


        private void BrowseClick(object sender, RoutedEventArgs e)
        {
            var fileDialog = new OpenFileDialog
                {
                    Filter = Filter, 
                    Multiselect = false
                };
            bool? showDialog = fileDialog.ShowDialog();
            if (showDialog == true)
            {
                Path = fileDialog.FileName;
                SetCurrentValue(PathProperty, fileDialog.FileName);
            }

        }

        private void PathTb_OnTextChanged(object sender, TextChangedEventArgs e)
        {
            Path = PathTb.Text;
            //SetCurrentValue(PathProperty, PathTb.Text);
        }

    }
}