The Brussels office will ensure that the company "will be able to write risks from all 27 European Union and three European Economic Area states after the United Kingdom has left the EU", Lloyd's said.
The new subsidiary will be "ready to write business" in time for the January 2019 insurance renewal season unless there are issues with regulatory approval, it said.
Lloyd’s chief executive Inga Beale said: "It is important that we are able to provide the market and customers with an effective solution that means business can carry on without interruption when the UK leaves the EU."
"Brussels met the critical elements of providing a robust regulatory framework in a central European location, and will enable Lloyd’s to continue to provide specialist underwriting expertise to our customers," she said.
The UK, Lloyd's said, "remains a full member of the European Union for at least two more years and therefore, there is no immediate impact on existing policies, renewals or new policies, including multi-year policies, written during this period of time".
Beale said: "It is now crucial that the UK government and the European Union proceed to negotiate an agreement that allows business to continue to flow under the best possible conditions once the UK formally leaves the EU. I believe it is important not just for the City but also for Europe that we reach a mutually beneficial agreement."
Lloyd's considered five different European locations for its subsidiary, chairman John Nelson said in December.
The subsidiary is likely to cost tens of millions of pounds to Lloyd's members due to high compliance and regulation costs and the market will change its plans if a deal between the UK and EU allows it to trade from London, Nelson told the Financial Times in December.
Lloyd's is lobbying strongly for a continuation of the current passporting regime. Passporting arrangements enable firms based in one EU member state to trade anywhere in the bloc without having to seek multiple authorisations. However, reports have suggested that this type of single market access would almost certainly require the UK to agree to freedom of movement of EU workers, and to comply with relevant EU regulations. Some financial contribution to the EU is also likely to be required, as is currently the case for the non-EU countries that form part of the European Economic Area (EEA), including Norway.