Her trip will also coincide with the signing of a £1.3 billion Swansea City Deal between the UK Government, local authorities and the Welsh Government, which aims to create more than 9,000 jobs in the region.
A spokesman for the European Commission said: "Everything is ready on this side".
"Next Wednesday, the Government will deliver on that decision and formally start the process by triggering Article 50". Strengthening May's hand to push for a so-called hard or clean Brexit is the British economy's defying of predictions that voting to leave the European Union would spark a recession.
An early flashpoint will be the bill Barnier wants to present Britain with.
First Minister Nicola Sturgeon has used this as one of the key reasons for seeking a Section 30 order to organise a second independence referendum. Other issues to be discussed early on include border issues and rights of European Union citizens residing in the U.K.as well as Britons living in the bloc.
Downing Street said Britain's ambassador to the EU, Tim Barrow, notified the EU of May's intention verbally.
British negotiators are sure to quibble over the size of that tab.
Negotiations will also soon hit a fundamental topic: Britain wants "frictionless" free trade, but says it will restore controls over immigration, ending the right of European Union citizens to live and work in Britain. The decision triggered the near-immediate resignation of the country's former Prime Minister, David Cameron, and.
That prospect alarms many British businesses. If no deal is reached by the end of the period, Britain will crash out of the European Union with no deal and revert to World Trade Organisation rules. Despite mutual threats of no deal, few want such chaos.
The EU said it was ready to begin the negotiations and within 48 hours of the trigger on March 29, Tusk will send the other 27 member states his draft negotiating guidelines, which means that talks could start in May. Some experts say the process could take a decade.