Ramsey is set to end an 11-year stay with the Gunners and make the switch to the Serie A champions when his contract expires in this summer. The midfielder has agreed a four-year contract with the Italian outfit and will team up with the likes of Cristiano Ronaldo, Paulo Dybala, Giorgio Chiellini and Leonardo Bonucci with the Italian champions.
But with the Serie A side set to pay just €3.7m to register Ramsey, Baresi sees the move as a brilliant one from a club who have dominated the league in recent years.
"I've seen him play. He's obviously a great player," he told the BBC.
"I think Juve has really landed a great coup there and I'm sure he'll be able to adapt to Italian football."
Baresi, who won six league titles in Italy, was full of praise for Juve's transfer business, but the Milan legend is also hoping their dominance in Italy will not last.
His former side sit 24 points back in fourth place in the table and are hoping for a Champions League place next term, though they face a tough challenge from the likes of Roma, Inter and Lazio as they look to hold in the top four.
And Baresi says it's down to the challenging sides to make the improvements needed to challenge Juventus at the top of the pile, with qualification for the Champions League crucial to sustaining growth.
"Juventus has owned Serie A in the last few years so it's important to see what the other teams can do in terms of growing," said Baresi.
"Teams like Inter, Roma, Milan, Lazio and Napoli are definitely all growing at the moment.
"Champions League qualification will be very important for Milan this year. It brings in money, it brings in opportunities for investment and chances to progress so it's important."