The former Los Blancos defender’s departure follows a final-day victory over Athletic Club, bringing an end to his short six-month spell in the Santiago Bernabeu dugout.
Mbappe was among the first players to contact Arbeloa after news of his exit, sending a message wishing him success in his future career away from Valdebebas.
The tactician, clearly moved by the message from the World Cup winner, responded with a glowing public tribute on social media.
“Thank you very much, Kylian Mbappe. I will always boast about having coached such an extraordinary football player with unparalleled talent. Tough times don’t last forever, but strong people do.”
Arbeloa led Los Blancos in 28 matches, recording 18 wins, two draws and eight defeats, but was unable to deliver any trophies during his short spell in charge.
The Spanish giants are now expected to appoint Portuguese manager Jose Mourinho as his successor ahead of next season.