Visa Inc. and MasterCard Inc. ended nearly two decades of European Union antitrust scrutiny with a pact that requires them to reduce fees for foreigners shopping in the region.

The EU dropped its final investigations months after fining MasterCard 570.6 million euros ($636 million) in another probe over payment rules. The April 29 settlement, which rubber-stamps a draft accord from December, sees the duo reduce levies for non-European card-holders charged on purchases in the 28-nation bloc.

“This, together with our...