Tusk has said that that once European Union officials get Britain's notification, they will respond within 48 hours, offering draft negotiating guidelines for the 27 remaining member states to consider.
Notification comes 279 days after the referendum of June 23 past year delivered a 52%-48% majority in favour of withdrawal.
Mrs May will meet First Minister Carwyn Jones as well as leaders in business and other areas, and will be accompanied by Brexit Secretary David Davis and Welsh Secretary Alun Cairns.
The spokesman said Britain wanted to start withdrawal negotiations "promptly", but accepts that "it is right that the 27 have a chance to agree their position" before talks start.
In Northern Ireland, which also voted to stay in the European Union, the largest Irish nationalist party, Sinn Fein, has said it wants a referendum on splitting from the United Kingdom and uniting with the Republic of Ireland "as soon as possible".More news: Authorities seal 2 slaughter houses in Allahabad
Actual negotiations might not start until June, they added.
Triggering Article 50 is required to start the process of leaving the European Union, although the negotiations could stretch out over years.
The prime minister has said that "now is not the time", and is expected to visit Scotland as part of a pre-Brexit tour of Britain that began on Monday in Wales and will also take in Northern Ireland. Former British ambassador to the EU John Kerr, who wrote Article 50, says "it is not irrevocable".
The Article 50 announcement came after Britain's envoy to Brussels, Sir Tim Barrow, informed Mr Tusk's office on Monday morning.
The European Commission's Brexit negotiator Michel Barnier has said they must be wrapped up by October 2018 to give the EU and national parliaments time to ratify the deal.More news: What we learned from the hearing on the Trump campaign's Russian Federation ties
THERESA May faces a fresh Brexit storm in Wales as she arrives to shore up support for the United Kingdom, ahead of pushing the Article 50 Brexit button.
"I want to be clear that a "no deal scenario" would be bad for everyone, but above all for the United Kingdom, because it would leave a number of issues unresolved".
Britain's exit negotiations are expected to be exceptionally tricky, with the country aiming to leave Europe's common market and customs union but hoping to retain preferential access to both through a new trading agreement.
Labour leader Jeremy Corbyn said: "The Government has failed to build a consensus about what form Brexit should take".
"We are on the threshold of the most important negotiation for this country for a generation".More news: Young Wildcats win to advance to Sweet 16
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