Here goes the Answer
Private Sub btnAssign_Click(ByVal sender As System.Object, ByVal e As System.Windows.RoutedEventArgs)
Dim btnAssign = TryCast(sender, Button)
If btnAssign IsNot Nothing Then
Dim columnUpdatedby As DataGridColumn = TaskDataGrid.Columns(15)
Dim columntimestamp As DataGridColumn = TaskDataGrid.Columns(16)
Dim feUpdatedby As FrameworkElement = columnUpdatedby.GetCellContent(TaskDataGrid.SelectedItem)
Dim fetimestamp As FrameworkElement = columntimestamp.GetCellContent(TaskDataGrid.SelectedItem)
Dim gridCmboUpdatedby As Grid = DirectCast(feUpdatedby, Grid)
Dim gridCmbotimestamp As Grid = DirectCast(fetimestamp, Grid)
Dim lblAssignedBy As Label = CType(gridCmboUpdatedby.FindName("lblAssignedBy"), Label)
Dim lblAssignedTimestamp As Label = CType(gridCmbotimestamp.FindName("lblAssignedTimestamp"), Label)
lblAssignedBy.Content = BCOMSCurrentUser.BCOMSUser.UserName
lblAssignedTimestamp.Content = DateTime.Now.ToString()
End If
End Sub