The pair clashed during halftime of the 2-1 win over Real Madrid in the first leg last month, with the bust-up delaying the signing of a new deal for Robben.
But Bayern said the 28-year-old Netherlands winger had signed a two-year extension, removing a potential distraction ahead of the Champions League final.
"I've always said that I feel very, very well in Munich and that's why I've extended my contract early,'' Robben said in a Bayern statement. "Bayern is like a family for me. Two of my three children were born in Munich, my family and myself feel at home here.
"It's the right decision from the sporting point of view, too. We have a great team and I am sure we are going to have the greatest possible success in the coming years.''
Bayern knocked out Madrid in a penalty shootout after the second leg at Santiago Bernabeu stadium also finished 2-1.
Bayern will play the Champions League final against Chelsea on May 19 at its own stadium.
The team will finish second in the Bundesliga and plays the German Cup final against league champion Borussia Dortmund.
"Arjen is a very important player for Bayern Munich and a guarantor for a successful future of the club,'' Bayern chairman Karl-Heinz Rummenigge said.
Robben had been unhappy, not only because of his feud with Ribery but also because Bayern chairman Franz Beckenbauer had called him "selfish.'' The often-injured player was also benched for a few games by coach Jupp Heynckes.
Speaking before Bayern announced the deal, Heynckes said Ribery had apologized and the club "has done what was necessary.''
"We have great targets and they can reached only with both of them in top form,'' Heynckes said.
Midfielder Bastian Schweinsteiger said Robben was highly regarded in the team.
"Every club would want to have such a player,'' Schweinsteiger said.
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