Your binding source must implement the IDataErrorInfo interface. Then you can set the ValidatesOnDataErrors and NotifyOnValidationError propeties on the binding.
See a simplified example below.
A base class to handle property changes and validation.
internal abstract class ValidatedObservableBase : INotifyPropertyChanged, IDataErrorInfo
{
    public event PropertyChangedEventHandler PropertyChanged;
    public string this[string columnName]
    {
        get
        {
            var results = new List<ValidationResult>();
            var valid = Validator.TryValidateProperty(GetType().GetProperty(columnName)?.GetValue(this), new ValidationContext(this) { MemberName = columnName }, results);
            return valid ? null : results[0].ErrorMessage;
        }
    }
    public string Error
    {
        get => null;
    }
    protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
    {
        PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
    }
}
The model, derived from the above base class.
internal class Model : ValidatedObservableBase
{
    private string number;
    [Required(ErrorMessage = "Required error")]
    [RegularExpression(@"^[\d]+", ErrorMessage = "Regex error")]
    public string Number
    {
        get => number;
        set
        {
            number = value;
            OnPropertyChanged();
        }
    }
}
A simple view model to set as the window's DataContext.
internal class ViewModel
{
    public Model Model { get; set; } = new Model();
}
Lastly, the window.
<Window
    ...
    xmlns:local="clr-namespace:Demo"
    mc:Ignorable="d">
    <Window.DataContext>
        <local:ViewModel />
    </Window.DataContext>
    <StackPanel>
        <TextBox
            x:Name="TB"
            Margin="24,24,24,0"
            VerticalAlignment="Top"
            Text="{Binding Path=Model.Number, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged, ValidatesOnDataErrors=True, NotifyOnValidationError=True}" />
        <TextBlock
            Margin="24,4,24,24"
            Foreground="Red"
            Text="{Binding ElementName=TB, Path=(Validation.Errors)[0].ErrorContent}" />
    </StackPanel>
</Window>
