One can use DataGrid InputBindings to achieve goal:

<DataGrid.InputBindings>
   <MouseBinding MouseAction="LeftDoubleClick" Command="{Binding SomeCommand}" />
</DataGrid.InputBindings>

You can apply the following behavior on data grid row and follow the usage for implementation.

Double Click Behavior

    public class DoubleClickBehavior
    {
        #region DoubleClick

        public static DependencyProperty OnDoubleClickProperty = DependencyProperty.RegisterAttached(
            "OnDoubleClick",
            typeof(ICommand),
            typeof(DoubleClickBehavior),
            new UIPropertyMetadata(DoubleClickBehavior.OnDoubleClick));

        public static void SetOnDoubleClick(DependencyObject target, ICommand value)
        {
            target.SetValue(OnDoubleClickProperty, value);
        }

        private static void OnDoubleClick(DependencyObject target, DependencyPropertyChangedEventArgs e)
        {
            var element = target as Control;
            if (element == null)
            {
                throw new InvalidOperationException("This behavior can be attached to a Control item only.");
            }

            if ((e.NewValue != null) && (e.OldValue == null))
            {
                element.MouseDoubleClick += MouseDoubleClick;
            }
            else if ((e.NewValue == null) && (e.OldValue != null))
            {
                element.MouseDoubleClick -= MouseDoubleClick;
            }
        }

        private static void MouseDoubleClick(object sender, MouseButtonEventArgs e)
        {
            UIElement element = (UIElement)sender;
            ICommand command = (ICommand)element.GetValue(OnDoubleClickProperty);
            command.Execute(null);
        }

        #endregion DoubleClick
    }

Usage

        <Style   BasedOn="{StaticResource {x:Type DataGridRow}}"
               TargetType="{x:Type DataGridRow}">
            <Setter Property="Helpers:DoubleClickBehavior.OnDoubleClick" Value="{Binding Path=DataContext.MyCommandInVM, RelativeSource={RelativeSource Mode=FindAncestor, AncestorType={x:Type ViewLayer:MyUserControl}}}" />
        </Style>

Not sure if you're going the MVVM route, but I've achieved this functionality using an Attached Command Behavior to wire up the double click event to a command in my viewmodel (where "command" is a reference to my attachedCommandBehavior assembly/class):

<DataGrid.RowStyle>
        <Style TargetType="{x:Type DataGridRow}">
            <Setter Property="command:CommandBehavior.Event" Value="MouseDoubleClick"/>
            <Setter Property="command:CommandBehavior.Command" Value="{Binding SelectItemCmd}"/>
            <Setter Property="command:CommandBehavior.CommandParameter" Value="{Binding }"/>
        </Style>
</DataGrid.RowStyle>