Do I have to pay back money I stole before becoming Muslim?

Yes, if you can. Becoming Muslim wipes out your sins against Allah, but scholars agree that other people's rights remain. If you took money or property from someone, try to return it, even quietly and anonymously. If you can't find the owner, give the same value in charity on their behalf. And if you can't afford it yet, pay a little at a time.

Two kinds of wrongs

Islam separates sins between you and Allah, like missed prayers before Islam, from wrongs done to people. The first are wiped clean by your shahada. The second involve someone else's rights, so they need to be put right where possible.

The Prophet Muhammad ﷺ said: "Whoever has oppressed another person concerning his reputation or anything else, he should beg him to forgive him before the Day of Resurrection when there will be no money" (Sahih al-Bukhari 2449).

This is explained further in Are all my sins forgiven when I become Muslim?

How to pay it back

If you know the person: return the money. You don't have to explain every detail. A simple "I owe you this" or an anonymous transfer works.
If it was a store or company: many scholars say you can pay the value back to the business, for example through a payment they won't trace to a theft.
If you can't find the owner: give the same amount to charity, intending the reward for them.
If you can't afford it now: make a plan and pay gradually. Allah sees your intention.

Do you have to confess to the police?

Most scholars say no. Islam encourages you to keep your past sins private and repent between you and Allah, while returning what you owe. If there's an ongoing legal case, get proper legal advice.

وَمَن يَعْمَلْ سُوٓءًا أَوْ يَظْلِمْ نَفْسَهُۥ ثُمَّ يَسْتَغْفِرِ ٱللَّهَ يَجِدِ ٱللَّهَ غَفُورًا رَّحِيمًا "And whoever does a wrong or wrongs himself but then seeks forgiveness of Allah will find Allah Forgiving and Merciful." Quran 4:110

Small things count too

Unpaid debts, things you borrowed and never returned, or money you cheated someone out of are all in the same category. Make a list, start with what you can, and keep going.

Don't let guilt crush you

Many converts feel ashamed about their past. Allah knows you've changed. Making things right is not a punishment; it's a chance to walk into your new life with nothing hanging over you.

Key points

Sins against Allah are forgiven at shahada.
Other people's rights still need to be returned.
Pay back quietly; anonymity is fine.
If the owner is unknown, give it in charity for them.

Tip: Write a private list of what you owe and to whom. Crossing items off, one by one, brings real peace of mind.