Both will face action for improper conduct on the pitch during Saturday's final which Real won 4-1 after extra time.
Simeone twice encroached on to the pitch during extra time and confronted Real defender Raphael Varane after the final goal before being restrained by the Atletico coaching staff.
Alonso, who missed the match through suspension, sprinted down the touchline after the match.
UEFA say their cases will be dealt with at disciplinary hearings on July 17 and both face suspensions from Champions League matches next season if found guilty.
UEFA have also charged both clubs for receiving at least five yellow cards during the match.
Seven Atletico players and five from Real were booked during a tempestuous encounter in Lisbon.