The UK's Serious Fraud Office (SFO) has spent the last 6 years chasing BAE systems over allegations that bribes were paid to secure foreign deals in a number of countries. Bribes are the least of the allegations involved in some international defense deals, and contract wins without inducements would be far more surprising in countries like Saudi Arabia, Tanzania, and South Africa. Nevertheless, the UK does have laws to prevent British firms from paying them, and the US Department of Justice chose to pursue the matter as well.
BAE Systems has settled with both governments, pleading guilty to technical violations but not criminal offenses, and paying about $400 million to the US DoJ, and GBP 30 million in the UK. I have the full history and details over at DID.
It will be interesting to see how future Saudi arms deals get done, given that bribes are a requirement.
Probably in partnership with Saudi firms, who will take care of the required bribes, all in return for slight adjustments in their workshare and payment rates over the life of the contract. Very likely even with partners and workshare/ recompense set, in part, by the Saudi authorities themselves as part of the deal. The foreign firms, whomever they may be, could end up becoming sub-contractors to Saudi firms, at least as far as the deal's official structure goes.
Anti-corruption laws do make a dent, but only in the small things, or in states without the combination of corruption and a culture of impunity. As long as they're determined to be corrupt on an official level, there will always be ways around it.
It will also be interesting to watch the consequences as more and more foreign firms from China, Brazil, Pakistan, India, South Africa, South Korea, Turkey, et. al. continue to enter the global market for high-end weapon systems. Many of those states (plus Russia, plus France) have very different ideas about global anti-corruption laws, and are unlikely to conform.
As choices expand in the global arms marketplace - a trend that is already irreversible - anti-corruption laws will be only one area where the West's ability to influence global military developments is going to decline.