Actually, none of the proposed solutions worked in my case (Python 2.7.6, NumPy 1.8.2). But I've found out, that change of dtype from complex (standard Python library) to numpy.complex_ may help:

>>> import numpy as np
>>> x = 1 + 2 * 1j
>>> C = np.zeros((2,2),dtype=np.complex_)
>>> C
array([[ 0.+0.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j]])
>>> C[0,0] = 1+1j + x
>>> C
array([[ 2.+3.j,  0.+0.j],
       [ 0.+0.j,  0.+0.j]])

This seems to do what you want:

numpy.apply_along_axis(lambda args: [complex(*args)], 3, Data)

Here is another solution:

# The ellipsis is equivalent here to ":,:,:"...
numpy.vectorize(complex)(Data[...,0], Data[...,1])

And yet another simpler solution:

Data[...,0] + 1j * Data[...,1]

PS: If you want to save memory (no intermediate array):

result = 1j*Data[...,1]; result += Data[...,0]

devS' solution below is also fast.

If you want to create an array containing complex values, you need to specify a complex type to numpy:

>>> A = np.zeros((3,3), dtype=complex)

>>> print A
[[ 0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j]]

>>> A[0,0] = 1. + 2.j

>>> print A
[[ 1.+2.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j]]

Python has built-in support for complex numbers. You can just enter them like that:

>>> a = 2 + 3j # or: complex(2,3)
>>> a
(2+3j)
>>> type(a)
<type 'complex'>
>>> a.real
2.0
>>> a.imag
3.0
>>> 

As for the container, in Python you can start with a list:

>>> complex_nums_list = [2+3j, 3+4j, 4+5j]
>>> complex_nums_list
[(2+3j), (3+4j), (4+5j)]

Or you can use numpy.array, which would be more suited for numerical applications.