After talks with Italian Prime Minister Paolo Gentiloni in Berlin, the leader of Europe's top economy said that the remaining EU member states would enter into the negotiations with London with a united front.
Merkel said that May's keenly anticipated address on Tuesday had provided a "clear impression of how Britain wants to move forward".
"However the negotiations would only begin when Article 50 is triggered," she told reporters, referring to the part of the EU's Lisbon Treaty under which a country officially declares its intention to quit the bloc.
Looking to Gentiloni, Merkel said that Germany and Italy would "closely coordinate" with each other and with "our respective industrial sectors" as the Brexit talks progressed.
"I am not worried that we won't stand together - the most important thing is that Europe won't let itself be divided and we will ensure this with very close contact," she said.
Gentiloni, speaking through an interpreter, said that May's speech had "put some meat on the bones" of the British position on leaving the European Union.
He pledged there would be "solidarity" among the other 27 EU member states but also "of course friendship" with Britain.
"I'd like to stress two things that are to me important and positive: that Theresa May recognized and underlined her support for international alliances and secondly that the agenda for Britain leaving will stick to the treaties," he said, citing the terms laid out in Article 50.
"There will be an agreement one day on this basis."
May on Tuesday said Britain would leave the EU's single market in order to restrict immigration in a clean break from the bloc but would seek a free trade deal giving "the greatest possible access" to the market on its departure.
But she warned that London would be free to change its economic model and "set competitive tax rates" if EU leaders insisted on a "punitive deal" for a trade pact with the bloc.