I've been able to get print statements redirected to a Tkinter text widget based on the answer to this question. It describes a class to redirect stdout:
class TextRedirector(object):
    def __init__(self, widget, tag="stdout"):
        self.widget = widget
        self.tag = tag
    def write(self, str):
        self.widget.configure(state="normal")
        self.widget.insert("end", str, (self.tag,))
        self.widget.configure(state="disabled")
Utilizing the TextRedirector class, I have the following code
import sys
import time
from tkinter import *
root = Tk()
t = Text(root, width = 20, height = 5)
t.grid()
old_stdout = sys.stdout
sys.stdout = TextRedirector(t)
for i in range(5):
    print i + 1
    time.sleep(1)
sys.stdout = old_stdout
However, this solution seems to be blocking (the text shows up all at once once the for-loop ends).
I have successfully put together a non-blocking solution using Popen and threading, but this isn't an ideal solution due to some unrelated constraints.
Is there a way to have the print statements show up in the text box in real-time?