Speak with a lawyer about your case before doing anything.
Most people who overstay their visa status by more than a year are subject, upon leaving, to a ten-year bar to coming back. This is because, from the expiration of their visa status, they begin building up a special kind of time out of status called "unlawful presence."
HOWEVER: you might not even be subject to this bar at all. People admitted for "Duration of Status ("D/S") on their I-94 cards - as are most J-1s and F-1s - don't start building up "unlawful presence" time, even if technically out of status, until some formal determination is made by an immigration officer or immigration judge that they are officially out of status. This may come in the form of a denial of a petition or application by immigration, a determination in deportation/removal proceedings, etc. An attorney will be able to tell you.
If it turns out you are subject to the bar, waivers are available but difficult to get - and can only be based on a very high level of hardship to U.S. citizen spouse or parent (if you don't have a U.S. citizen spouse or parent, there's no possibility of a waiver).
You also need an attorney to look into your J-1 visa and make sure you aren't subject to the requirement that you spend two years in your country of last residence before returning to the U.S. Since your change of status to F-1 was approved, you likely aren't - but this should still be checked by an attorney.
Glad to help! Not sure I did understand you right though - I thought when you said you "overstayed your visa" you meant you were here for a year without still being properly enrolled in your F-1 program. Staying past the date on the visa stamp in your passport isn't "overstaying" - which is normally taken to mean being out of status. The passport stamp doesn't control valid status in the U.S., only your ability to apply at a border point for entry into the U.S.
Further to Stu's excellent answers above, although F-1 and J-1 nonimmigrants are not accruing "unlawfully presence" (i.e. deemed to have overstayed) until/unless there is a formal determination made by USCIS or ICE that their F or J status has terminated - not just staying past the end date on an I-20 or a DS-2019 - it is easier for the government to make such a determination than it used to be, because all F-1 students and J-1 exchange visitors have to register for the SEVIS database. SEVIS is updated by the responsible person at the school, whenever you start or end a program, drop out or drop below a full courseload, get authorization to work off-campus, etc.
If you have always maintained a full courseload and have not violated your J-1 of F-1 status, then it is not clear what you mean by your post:
1) Do you just mean that the visa stamp in your passport has expired, even though your I-20 is current? That is not an overstay! The visa itself is only an entry document, and is valid for seeking admission when you are entering the US from abroad. Once you are admitted to the U.S., the document that determines the validity of your period of stay is the I-94 admission card, and for F-1 or J-1 nonimmigrants, it is issued for "D/S", or duration of status. The duration of your status is defined by the authorizing program documents - the Form DS-2019 for a J-1, or the Form I-20 for an F-1. If this is what you meant, then you have not accrued any overstay at all, and simply need to apply for a new visa the next time you travel abroad, with all the documentation that you have maintained valid J-1 and F-1 status since you began attending school in the US.
2) If that is not the case, do you mean that you had a previous overstay of a year or more after an entry in some other visa status, prior to beginning your studies? You really need to clarify this by meeting with an immigration attorney in person and having the attorney examine your original documents: your passport, visa(s), I-94 card, and all your DS-2019 and I-20 forms.
This is general information only. It is not intended as a substitute for legal advice, and does not create an attorney-client relationship.