Donald Trump has been urged to commit to strengthening relations with the European Union, including on Russia's actions in the Ukraine and the future of the troubled US-EU trade deal.
European Council president Donald Tusk and his European Commission counterpart, Jean-Claude Juncker, invited Mr Trump to visit Europe for a summit meeting with the EU.
They offered their "sincere congratulations" to the new US president-elect and stressed it was "more important than ever" to work together to tackle problems including Islamic State, also known as Daesh.
The two leaders said: "The strategic partnership between the European Union and the United States is rooted in our shared values of freedom, human rights, democracy and a belief in the market economy. Over the years, the European Union and the United States have worked together to ensure peace and prosperity for our citizens and for people around the world.
"Today, it is more important than ever to strengthen transatlantic relations. Only by co-operating closely can the EU and the US continue to make a difference when dealing with unprecedented challenges such as Daesh, the threats to Ukraine's sovereignty and territorial integrity, climate change and migration.
"Fortunately, the EU-US strategic partnership is broad and deep: from our joint efforts to enhance energy security and address climate change, through EU-US collaboration on facing threats to security in Europe's eastern and southern neighbourhoods, and to the negotiations on the Transatlantic Trade and Investment Partnership - we should spare no effort to ensure that the ties that bind us remain strong and durable.
"We should consolidate the bridges we have been building across the Atlantic. Europeans trust that America, whose democratic ideals have always been a beacon of hope around the globe, will continue to invest in its partnerships with friends and allies, to help make our citizens and the people of the world more secure and more prosperous.
"We would take this opportunity to invite you to visit Europe for an EU-US summit at your earliest convenience. This conversation would allow for us to chart the course of our relations for the next four years."
European Parliament president Martin Schulz expressed surprise at the result, saying it had been "another Brexit night".
"We are seeing a wave of protest against established politics which is also reflected in this election result," he said.