Vidal flew to Italy on Sunday ahead of a transfer to the Nerazzurri and the deal, which will cost around €2 million, should be completed early this week.
"I only knew you from when we played against each other and I always thought you were a phenomenon," Messi wrote on Instagram alongside a picture of them both at Barca's training ground.
"But later I had the chance to get to know you personally and you surprised me further still. We have shared many things these two years and you made your presence felt greatly.
"The dressing room is going to miss you."
And he added: "I wish you all the best in this new stage with your new club. We will meet again, I'm sure."
— Inter (@Inter_en)September 20, 2020
Inter also posted a tweet on Sunday telling their fans that the 33-year-old had arrived in Milan.
Vidal played 96 official games for Barcelona in two seasons, scoring 11 goals and winning two trophies during his time at Camp Nou.