The 35-year-old Hungarian made his international debut in 2001 and has officiated more than 60 UEFA matches in his career.
Kassai has handled one Europa League and five Champions League games this season, including the first leg of the last 16 match between Inter Milan and Bayern Munich and the group-stage match between Valencia and Manchester United.
Kassai will be assisted by fellow countrymen Gabor Eros and Gyorgy Ring. The fourth official will be Istvan Vad.
The final will be played Saturday at Wembley Stadium.