Negotiations between the two companies have dragged on for months as the parties debated who should lead the efforts to develop an engine for the strategic Franco-German project.
But in a statement on Tuesday, the companies agreed Safran would be "prime contractor" - a term typically used in the defence industry for the company running a project - with MTU billed as "main partner" during the initial research phase.
The two firms will then set up a 50/50 venture by end-2021 to manage later stages of the project, including development, production and after-sales support of the new engine.
Safran will take the lead in engine design and integration, and MTU will take the lead in engine services, they said.
There had been reports of concerns in Germany's parliament over Safran being awarded the lead engine role in the project, which was announced by French President Emmanuel Macron and German Chancellor Angela Merkel in 2017 to deepen defence ties.
Britain, with Swedish and Italian support, has embarked on a rival European fighter project called Tempest, while Spain has signed up to the Franco-German "Future Combat Air System".
(Reporting by Sudip Kar-Gupta, Tim Hepher, editing by Louise Heavens and Alexandra Hudson)