Europe's leading clubs are to receive an increased 100 million euros from the proceeds of Euro 2012 in Ukraine and Poland in June and July.
That rise will go up to 150 million euros for the 2016 finals in France when the tournament is expanded from 16 to 24 teams.
"I am a very happy man that we have managed to unify the entire football family," Platini told a news conference.
"I am delighted we have brought together the key stakeholders and have shown unity on several important matters which affect international football."
As well as signing a new Memorandum of Understanding with the ECA, European football's governing body also penned new agreements with the European Professional Football Leagues (EPFL) and FIFPro, the worldwide players organisation.
FIFA President Sepp Blatter joined in the celebratory mood and promised football's ruling body would follow UEFA's lead by setting up insurance policies for players called up for international duty.
Rummenigge, a West German international who played against Platini's France in the 1980s, joked the two men had enjoyed another battle off the field.
"Today is an excellent day," he told delegates at the 36th annual UEFA Congress. "It proves there is harmony, loyalty and fairness in European football."
Rummenigge also called on Blatter to come to an agreement with the 201-member ECA.
"Please open the door to FIFA," he said although football's ruling body previously underlined that its door was always open but that Rummenigge had decided not to walk through it.
The German declined to attend a meeting at FIFA earlier this month but Blatter offered the clubs an olive branch when he addressed Congress.
He said FIFA would pay for "total insurance coverage" for international footballers in official matches, adding: "You have to take into account the best interests of the players".
The policy is likely to come into effect after the FIFA Congress in Budapest in May and be in place for the start of the European qualifiers for the 2014 World Cup in September.
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