Metsola is only the third woman elected to the post and at age of 43 she is the European Parliament's youngest president.
Sassoli, 65, had been sick for several months, and before his death the Italian politician declined to seek another term.
Metsola was the candidate of the parliament's biggest group, and she received 458 of the 616 votes cast Tuesday. She had already been acting president since Sassoli's January 11 death.
She will lead an EU institution which has become more powerful over the years and been instrumental in charting the course of the 27-nation bloc on issues such as the digital economy, climate change and Brexit.
The European Parliament represents the EU's 450 million citizens and refers to itself as "the heart of European democracy."
Known as a committed bridge-builder between parties, Metsola said she would stick to Sassoli's style of work.
"David fought hard to bring people around the same table. It is that commitment to holding the constructive forces in Europe together that I will build on," she said.
And she referred to giants of European post-war politics like German Christian Democrat Helmut Kohl and French Socialist Francois Mitterrand to overcome party divisions and give her guidance.
"My appeal is to rediscover the purpose of Kohl and Mitterrand and leave behind the entrenchment of the past as we look to the future," she said.
The parliament has long been the lesser EU institution compared to the executive European Commission and the European Council, which represents the governments of the 27 member states.
For many years, the parliament, which sits in Strasbourg, France, and Brussels was seen as a money-guzzling talking shop where politicians who had served their national purpose often were sent.
As it gained decision-making powers, though, the legislature it has become a more forceful player on the European scene. Metsola wants to continue that trend.
"We need to strengthen it. We cannot be afraid of reform," she said. "The next part of the mandate will see a window of opportunity to make our parliament more modern, more effective and more efficient. We must seize the opportunity."
Metsola is the first politician from Malta, a Mediterranean archipelago in the central Mediterranean with a population of just over half a million people, to hold such a high position in the EU.
"I am a woman from a small island in the middle of Europe's southern sea. I know what it means to be the underdog. I know what it means to be pigeonholed," she said. "I know what this means for every girl watching today. I know what it means for everyone who dares and whoever dared to dream."
