The two groups have decided to create what they call a "pro-European coalition to reform Europe."
It means the ALDE group will back Antonio Tajani, the EPP group candidate for the Parliament presidency. The Italian is now the strong favourite for the post.
A statement issued on Tuesday by the two groups reads, "As part of this political agreement, both groups will back Antonio Tajani to become President of the European Parliament."
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ALDE group leader Guy Verhofstadt, who withdrew his own candidacy for the presidency job at the last minute, said, "This is a first important step in the construction of a pro-European coalition to reform and strengthen our Union, which is absolutely necessary.
"With Trump, with Putin, with many other challenges Europe faces, it is key we cooperate to reform our Union."
The former Belgian Prime Minister said, "Our coalition plan is open to all pro-European groups. It's a coalition of ideas to change the direction of the EU. The agreement entails a European border and coast guard. A new governance for the eurozone to lift us out of the crisis.
"A European defence force to make Europe safe again. And we agreed also to examine whether a European intelligence and investigation capacity is necessary to fight terrorism and international crime."
Last Tuesday, Verhofstadt told a hearing of candidates that he predicted that the grand coalition - the agreement between the EPP and S&D groups which traditionally has seen the two groups share the presidency over the five year mandate of Parliament - would resume "within a week" of the election.
Further comment came from EPP group Chair Manfred Weber, who said, "The EPP group has always been pushing for an approach that is based on partnership - we remain true to that principle and will continue to deliver.
"We want to act together to bring results for European citizens and guarantee Europe's stability. Our partnership is based on content and on reforms for Europe. It is a pact for results."
A parliamentary insider said, "This agreement is effectively a grand coalition Mark 2. It is laughable. Instead of a pact between the EPP and Socialists we now have a pact between the EPP and ALDE."