Nice approach! Here is another option to do this ...

''' tk_button_toggle2.py
use a list default argument to create a Tkinter toggle button
'''

try:
    # Python2
    import Tkinter as tk
except ImportError:
    # Python3
    import tkinter as tk

def toggle(tog=[0]):
    '''
    a list default argument has a fixed address
    '''
    tog[0] = not tog[0]
    if tog[0]:
        t_btn.config(text='False')
    else:
        t_btn.config(text='True')

root = tk.Tk()

t_btn = tk.Button(text="True", width=12, command=toggle)
t_btn.pack(pady=5)

root.mainloop()

So we are spending our time on simple toggles huh. This uses a list so the function has access to the previous setting. I was too lazy to create a class with an instance variable.

try:
    # Python2
    import Tkinter as tk
except ImportError:
    # Python3
    import tkinter as tk

def toggle():
    index_dict={"True": "False", "False": "True"}
    index[0] = index_dict[index[0]]
    t_btn['text'] = index[0]

root = tk.Tk()
index=["True"]
t_btn = tk.Button(text=index[0], width=12, command=toggle)
t_btn.pack(pady=5)

root.mainloop()

Just one more ...

''' tk_button_toggle4.py
using itertools.cycle() to create a Tkinter toggle button
'''

import itertools
try:
    # Python2
    import Tkinter as tk
except ImportError:
    # Python3
    import tkinter as tk


def toggle():
    #global icycle
    # works with Python27 and Python3
    state = next(icycle)
    t_btn['text'] = str(state)

root = tk.Tk()
icycle = itertools.cycle([False, True])
t_btn = tk.Button(text="True", width=12, command=toggle)
t_btn.pack(pady=5)

root.mainloop()

This deserves an answer:

''' tk_button_toggle5.py
'''

from functools import partial
import itertools
import sys
python2 = sys.version_info[0] == 2
tk = __import__("tT"[python2] + "kinter")

def toggle(button):
    button.state = not button.state
    button['text'] = str(button.state)

def new_btn(state):
    btn = tk.Button(width=12)
    btn.state = bool(state)
    btn.config(text= str(btn.state), command = partial(toggle, btn))
    btn.pack(pady=5)
    return btn    

root = tk.Tk()
for x in (1, 0, 1):
    new_btn(x)

root.mainloop()

Notice that btn.state can now be accessed directly.

Vegaseat's code more elegant:

''' tk_button_toggle6.py
using itertools.cycle() to create a Tkinter toggle button
'''

import itertools
try:
    # Python2
    import Tkinter as tk
except ImportError:
    # Python3
    import tkinter as tk


def toggle(icycle=itertools.cycle([False, True])):
    state = next(icycle)
    t_btn['text'] = str(state)

root = tk.Tk()

t_btn = tk.Button(text="True", width=12, command=toggle)
t_btn.pack(pady=5)

root.mainloop()