There is no perfect answer to this. No magic bullet. And it's probably not possible for a single politician to eliminate corruption, especially in a way that will be lasting after he leaves office. It requires major changes to culture, political systems, and so on.
But there are ways to reduce corruption. The basic idea is, you need to have systems of inducements and ethics that will reinforce and feedback on each other so that when people do the right thing they get rewarded. When they do the wrong thing they get punished. And these need to happen automatically through the existing features of the system.
Many cultures do very much the opposite of this. They reward people who violate the ethics, and punish them for following the ethics. There is a fundamental reason for this. One exploration of this is this book by Jane Jacobs.
The best I can do here is a drastically abbreviated outline. The fundamental thesis in Jacobs's book is as follows. There are two very different systems of ethics. One applies to commercial activity like business, jobs, and various other activities associated with voluntary trade for profit. The other system applies to what Jacobs calls guardian activity. Guardian activities consist of getting hold of, and keeping hold of, geographic territory, and extracting value from that territory.
So the result is, if you stick to the ethical system that corresponds to your type of activity, then that system will reinforce itself and strongly discourage corruption. But if you get outside your system of ethics, then things go wrong very quickly.
Jacobs gives a page-long list of ethical rules for each system. Here I give just a few items that naturally show up as pairs.
On the commercial side the first rule is to shun force. On the guardian side the first rule is to shun trade.
I anticipate lots of people saying OH OH OH! Everybody should shun force and do trade! But look. A police officer necessarily wields force. Or at least the implication of force, the possibility of force, the threat of force. A cop who starts wanting to do "commerce" as part of his police activities is pretty much automatically corrupt. Imagine him bargaining over how much your traffic ticket should be because he gets paid on the basis of the ticket. While he stands at your car window with a gun on his hip.
So as long as we have both force and trade in society, they should be performed by two different groups. Because force is not compatible with free trade.
Another pair of rules:
On the commercial side, be optimistic. On the guardian side, be fatalistic.
Optimism means you expect things to get better, you expect newly met people to be valuable and useful trade partners. So you are likely to work hard and invest. Fatalism associates with your territory. Your home territory is your fate.
One last pair I will quote:
On the commercial side, pile up treasure. On the guardian side, treasure honor.
So just a couple examples. Consider the Mafia. They pull items from both lists. They have an honor code and definitely use force. But they also like to get a lot of money and do business trades. Result, a system that most people would agree is corrupt. They deal in bribes and threats and violence, but also have a public face that appears to involve legitimate businesses.
Consider what happens when you give police officers a financial incentive. For example if you pay them according to the number and prestige of arrests they make. Jacobs reports on such a scheme. When this was announced to the detectives, they were not out of the squad room before they had a scheme to plant drugs on motorists so they could then arrest them.
Consider prison operated factories. They pay the prisoners in the range of 10 cents an hour to make fridges and furniture and things. But that means they want a lot of relatively easy to manipulate prisoners. So, where did the "three time loser" law come from that will put somebody in prison for 25 years if he gets caught shoplifting 3 times? I'm not sure what the correct thing to do with such a person is, but I strongly suspect 25 years in prison is sub optimal. And why is the "war on drugs" so resilient? What happens to somebody who gets caught with a month's worth of pot? In some states, it's a very long prison term.
Jacobs gives several other examples, plus lots of interesting analysis. The basic result is, people who do the guardian actions in society should be well and truly separated from people who do commercial things in society.