I've just switched from my task manager Wunderlist to paid version of Todoist and I needed to transfer my tasks. My tasks are pretty easy, no complicated structures and subtasks (actually, not full-featured subtasks support in wunderlist is reason why I switched).

Todoist has unfortunately horrible support for import and you have basically the only option and that is to use txt file in todoist format for every project (list/folder in Wunderlist) separately.

Great post here helped me lot, where one of the users reverse-engineered the format. Here is the output:

{ 
[{"..."}][*]<task-name> 
[{" @"<label-name>" "}] 
["[[Date "<date-text>"]] "] 
["[[priority"(1|2|3|4)"]]"] 
[{"[[Note]]: "{<note-text>#x0A}#x09}] 
["[[Note]]: "<file-url>" ("<attachment-name>")"#x09] 
} 

(*syntax note: 

{} repeatable / nested text 
[] optional text 
"" string literal 
#x hex char 
concatenation is assumed 

*)

and example:

Task1-with-subtasks @label1 @label2 [[date 19 July]] [[priority 1]]  
...subtasklevel2 
......subtasklevel3 
.........subtasklevel4 
Task2!!BOLD!!and__ITALIC__can-be-used  
Task3-with-notes  
[[NOTE]]: Note1/Line1 #x0A Note-1/Line2 #x09 
[[NOTE]]: Note1/Line1 #x0A Note-1/Line2 #x09 
[[NOTE]]: Note1/Line1 #x0A Note-1/Line2 #x09 
Task4-attachment-example  
[[NOTE]]: https://hw44hkfs.cloudfront.net/2dffe7cb0e/as/test.txt (test text file)

All I needed was to export the following for every uncompleted task (and you might edit it to your needs):

1. Title
2. Due date (if applicable)
3. Note
4. Folder (which is called projects in Todoist)

Step by step solution

1. Export data from Wunderlist. Click on your account -> account -> Create backup. It downloads quite OK json formatted file.
2. Now you need to read the downloaded json file, extract informations about tasks and convert them to todoist txt format. Here is what I ended up doing. It's spaghetti code, but I am not ashamed of that, since it's just for one-time-shot usage and polishing would mean losing my time.

# load and read the file
with open("path-to-your-wunderlist-exported-file.json") as ifile:  
    import json
    data = json.load(ifile)["data"]

def extr(task):  
    # extracts all information I want from task
    title = task["title"]

    # dates have its own format for todoist
    if "due_date" in task.keys():
        from datetime import datetime
        due_date = "[[date " + datetime.strptime(task["due_date"], '%Y-%m-%d').strftime("%d %b %Y") + "]]"
    else:
        due_date= ""

    # notes are stored in different part of data dictionary - notes
    note_orig = [i["content"] for i in data["notes"] if i["task_id"] == task["id"]]
    if note_orig != []:
        note = "[[NOTE]]: " + "\t".join(note_orig[0].split("\n"))
    else:
        note = ""

    return title, due_date, get_list_by_id(task["list_id"]), note

def get_list_by_id(idecko):  
    return [i for i in data["lists"] if i["id"] == idecko][0]["title"]


# running logic
import operator  
# extract info about tasks which aren't completed yet
prepr = [extr(i) for i in data["tasks"] if i["completed"] == False]  
prepr.sort(key=operator.itemgetter(2))


# this part of code will create appropriate strings and saves
# them to files with project names
resul = {}  
for list_name in set([i[2] for i in prepr]):  
    #print("\n------{}------".format(list_name))
    s = ""
    for task in [task for task in prepr if task[2] == list_name]:
        if task[3] != "":
            s += "{} {}\n{}\n".format(task[0], task[1], task[3])
        else:
            s += "{} {}\n".format(task[0], task[1])
    resul[list_name] = s

for project, outp in resul.items():  
    with open(project + ".txt", "w") as ofile:
        ofile.write(outp)

Now you must create new project in Todoist and click on tools button on top right of adding new tasks. Click on Import from template and choose an appropriate file. Tasks should be imported :) .