The Denmark international – who joined Milan initially in January having been on loan at Atalanta earlier this season – moved to the Andalusian club from Turkish side Fenerbahce in 2017 and had made 64 first-team appearances for Los Rojiblancos in the time since before exiting on loan last summer.
Kjaer is a hugely experienced defender who can count Palermo, Wolfsburg, Roma and Lille among his former clubs before spending two years in Turkey between 2015 and 2017.
He has made 13 appearances for the Rossoneri and Marca now outline how the move has been made official following the agreement of all parties.
That purchase option was included in the loan deal, while it must also be remembered that Sevilla are now obliged to complete the permanent signing of winger Suso from the Italian club.
Suso joined Sevilla initially on loan and now that Sevilla have qualified for the Champions League, they must exercise their €21m option to sign him permanently.