"Europe has taken on its responsibilities. It has been able to do this but with conditions and with rules, and that is what France has called for," Hollande told reporters.
Europe has been struggling to coordinate a united response to an unprecedented influx of migrants and refugees from war-torn countries such as Syria.
"Couldn't we manage 120,000 in a continent with 450 million people? We will show that we can do this, and at the same time have rules. That is taking responsibility, that is solidarity," Hollande added.
The plan was bitterly opposed by the Czech Republic, Hungary, Romania and Slovakia, who argue that the European Commission does not have the right to make them take in people seeking refuge.
Asked about the possibility of sanctions for countries which did not respect Tuesday's agreement, Hollande said Europe had "rules".
"When you are in the European Union, it comes not just with benefits, it also means playing your part, especially when it comes to accommodating people who are in an extremely difficult situation," he said.
The agreement came on the eve of a key EU summit on Wednesday which is dedicated to finding ways to help countries to stop the flow of asylum seekers at sources.
Hollande's remarks came as the first refugees from war-torn Syria arrived in Britain, which is exempt from EU asylum and migration policy.
Hollande defended Britain's opposition to being part of a quota system, noting that it was "not in the Schengen area" of passport-free movement.
"But the United Kingdom will play its part as well in the reception of refugees, in particular in so-called resettlement," Hollande said.
British Prime Minister David Cameron has agreed to accept 20,000 refugees by 2020, from camps in countries bordering Syria such as Turkey and Jordan.
Hollande is on a diplomatic visit to Britain, and spoke before meeting Cameron at Chequers, his official country residence where the two will hold talks and a working dinner.