Von der Leyen acknowledged she was "worried" about the spread of the Delta variant, saying it was "only a matter of time" before it became dominant in Europe.
The supply cuts delayed the EU's vaccination drive in the first quarter of the year, when the bloc had initially bet on AstraZeneca to deliver the largest volume of its shots.
The court said in a statement that AstraZeneca must deliver 15 million doses by July 26, another 20 million by Aug. 23 and another 15 million by Sept. 27, for a total of 50 million doses.
Negotiated in marathon talks by EU and US officials, the truce will be formalised in Biden's summit with European leaders Charles Michel and Ursula von der Leyen.
The Europeans will be trying to clear the slate of trade disputes in order to enter a more friendly phase and jointly tackle other issues, which also include curbing big tech and handling Russia.
"Both sides must implement what we agreed on," von der Leyen, European Commission president, said after meeting Johnson alongside Michel, the European Council president.
"There is complete EU unity on this," she said, adding that the deal had been agreed, signed and ratified by both Johnson's government and the bloc.
"We aim to have offered a jab to 70% of all adults by the end of July...this is almost the same target as the one the US has set," she told a conference.
"Others are keeping their entire vaccine production all to themselves, but the EU will reach its vaccination targets without sealing itself off from the world."
"The EU is also ready to discuss any proposals that addresses the crisis in an effective and pragmatic manner," she said in a speech to the European University Institute in Florence.