The 51-year-old has been heavily linked with the vacancy at San Siro following Gennaro Gattuso's departure last month.
Giampaolo joined Sampdoria in 2016 from Empoli and guided them to 11th, 10th and ninth-place finishes respectively during his three seasons at the club.
He had been contracted until June 2020, but the club confirmed on Saturday that he has left the Stadio Luigi Ferraris along with his backroom staff.
Giampaolo told the club's official website: "I thank the president and everyone at Sampdoria for three incredible seasons.
“I had a good time in Genoa, and we had a good time together.
"My thanks to all the managers, collaborators, employees and players of the club. You remain in my heart like all Sampdoria fans."
Sampdoria president Massimo Ferrero went on to add: "We thank Marco for the three seasons with us.
“We grew up together, we enjoyed a lot of satisfaction and now we wish him good luck for the continuation of his career."
If Giampaolo does join Milan, he will link-up with legendary defender Paolo Maldini and Zvonimir Boban, who were named as the club's new technical director and chief football officer respectively on Friday.
I Rossoneri have been on the lookout for a new man at the helm after Gattuso announced his departure following the club’s failure to qualify for 2019/20 UEFA Champions League as they finished fifth.
Giampaolo will have the tough task of leading Milan back to their glory days on his hands, with the red and black half of the San Siro not seeing success in the league since winning the Scudetto in 2011.
The Italian spent one season with Empoli prior to joining Sampdoria, taking the club to a 10th-place finish in Serie A.
He is set to become Milan’s eighth manager in just over five years and will hope to avoid becoming the latest casualty in the merry go-round, with only Vincenzo Montella winning silverware in 2016 in the form of the Italian Super Cup.