You can do it like this:
Dim doubleAry As Double() = Array.ConvertAll(TextLine.Split(vbTab), New Converter(Of String, Double)(AddressOf Double.Parse))
However, if the string array that you are giving it contains any invalid items, that will throw an exception and fail to convert any of the items. If you want to handle invalid items and just default them to 0, you could implement your own converter, like this:
Private Function DoubleConverter(ByVal text As String) As Double
Dim value As Double = 0
Double.TryParse(text, value)
Return value
End Function
Then, you can use it like this:
Dim doubleAry As Double() = Array.ConvertAll(TextLine.Split(vbTab), New Converter(Of String, Double)(AddressOf DoubleConverter))