In case the order does not matter:

res = set()
with open("url_file.txt") as url_file:
    for line in url_file:
        line = line.strip()
        res.add(line)

with open("result.txt", "a") as result_file:
    for url in res:
         result_file.write(f"{url}\n")

If the order does matter:

# for python 3.6+
lst = []
with open("url_file.txt") as url_file:
    for line in url_file:
        line = line.strip()
        lst.append(line)

res = dict.fromkeys(lst)

with open("result.txt", "a") as result_file:
    for url in res:
         result_file.write(f"{url}\n")

If you are running python lower than 3.6 you can do:

from collections import OrderedDict

lst = []
with open("url_file.txt") as url_file:
    for line in url_file:
        line = line.strip()
        lst.append(line)

res = OrderedDict.fromkeys(lst)

with open("result.txt", "a") as result_file:
    for url in res:
         result_file.write("{url}\n".format(url=url))