Wrote is the simple past and stands alone: "she wrote the report." Written is the past participle and needs a helper: "she has written the report", "the report was written." The test is the same one that separates took from taken — look for the helper verb.
The core difference
Both are past forms of write, distinguished by whether a helper verb is present.
- wrote — no helper: He wrote back the same day.
- written — with have/has/had: He has written back.
- written — passive, with be: The letter was written in haste.
Written as an adjective
Written also works as a plain adjective where wrote never can: a written agreement, written English, put it in writing. That use is unrelated to the helper-verb rule and is another reason the two are not interchangeable.
The test
Look for have, has, had, was or were. If one is there, use written.
Frequently asked questions
Is "I have wrote" correct?
No. It should be "I have written". After have, has or had you need the past participle.
Which is right: it was wrote or it was written?
It was written. A passive takes a form of be plus the past participle.
Can written be an adjective?
Yes — a written agreement, written English. Wrote cannot be used that way.