The Chile international has spent two seasons at Barcelona and helped the club win La Liga in his first campaign at Camp Nou.
But Barca’s hierarchy have been seeking to offload several senior players this summer, including Vidal, Luis Suarez and Ivan Rakitic, in order freshen up the squad following a poor season which ended in an 8-2 defeat to Bayern Munich in the Champions League last month.
Vidal arrived in Milan on Sunday evening and will put the finishing touches on his €1 million (£900,000) move to Antonio Conte’s side on Monday.
But Messi admits Vidal’s departure will be felt in Barcelona’s dressing room.
‘I only knew you from facing each other and you always seemed like a phenomenon to me, but later I was lucky to meet you personally and you surprised me even more,’ Messi wrote on Instagram.
‘They were two years sharing many things and you made yourself heard a lot, the players are going to miss you, Arturo.
‘I wish you all the best in this new stage at your new club. We will cross again, for sure.’
Speaking last month, Vidal criticised Barcelona’s board for their failure to build a competitive squad.
‘Barcelona first have to change the way they think because football has evolved a lot,’ the 33-year-old said.
‘DNA is being left behind and other teams are improving in other aspects.
‘Nowadays, football is more physical, more about strength and speed, and technical ability can sometimes come second.
‘Barcelona have to change lots of things.
‘A club, which I think is the best in the world, can’t have 13 professional players and the rest youngsters.
‘Not because they don’t deserve to be there, but they have to be competing with the best and with who has to play.’