She will contact Tusk directly to launch negotiations in due course.
An EU spokesman said it was "ready and waiting" for the letter. Her spokesman, James Slack, rejected the idea of an early election on Monday, telling reporters: "There isn't going to be one".
Earlier, Downing Street (street where official residence of PM present) sources said with conviction that May would trigger Article 50 (mechanism to formally leave EU) by the end of March. The EU will then take some time to finalise its negotiating position.
While May says "no deal for Britain is better than a bad deal for Britain", quitting the bloc without a pact or more time to negotiate one would leave the country exposed to World Trade Organization tariffs, putting duties of around 10% on vehicle exports alone.
"The government is clear in its aims: a deal that works for every nation and region of the United Kingdom and indeed for all of Europe - a new, positive partnership between the United Kingdom and our friends and allies in the European Union", Davis added.
The UK expects to receive a response to Barrow's notification from the EU Council within 48 hours, he added. European Union leaders plan an initial response within two days before convening a summit to ratify guidelines for their chief Brexit negotiator, Michel Barnier. Under this scenario, talks are likely to begin in earnest in May.
"On the first day after withdrawal there will be convergence - we are creating something different", he told the Commons European Scrutiny Committee.
Mrs May said past year that she meant to notify the European Union of the UK's intention to leave by the end of March.
IFG's research director, Dr Hannah White, told BBC Radio Four's Today programme: "The estimates we have heard are something between ten and 15 Bills required in the next two parliamentary sessions".
European leaders have also been clear that Britain cannot get a better deal outside the EU than it had inside, amid fears that Brexit could cause other nations to leave the bloc.
Mrs May has said MPs and peers will have a vote on the deal she negotiates but she has insisted the United Kingdom will leave anyway even if Parliament rejects it.
But Sir Tim said such "speculation" was based on the difficulty of striking deals between countries with very different trade systems, when Britain and the European Union already had "convergence".
"The taoiseach has previously expressed impatience over the lack of clarity from Britain on Brexit", said Mr Adams. Even if that overstates what is involved, there is a significant possibility (close to a certainty, really) that there may have to be transitional arrangements after the formal Brexit date (there have been suggestions that these might have to last for as long as ten years) as everything falls or is shoved into place.
Britain's Prime Minister Theresa May.
May has signaled she will prioritize Britain's ability to control immigration from European Union countries, a critical element in driving pro-Brexit sentiment.
"Leaving the single market was not on the ballot paper in the referendum, it is a political choice made by Theresa May", he said. Mrs May is not attending the event.