The Serie A champions won the competition in 1985 and 1996, but have since lost in four finals. They were defeated by Borussia Dortmund in 1997, Real Madrid in 1998, AC Milan in 2003, and Barcelona in 2015.
However, on the domestic front Juve have collected five consecutive Serie A titles, and Vialli believes they now deserve to claim Champions League honours as well.
Juve take a 3-0 lead into the second leg of their quarter-final tie with Barcelona, whom they face in Spain on Wednesday.
Vialli told Gazzetta dello Sport: "Juve are instead in a time of stability and effectiveness, and they seem to have fun when they play.
"I believe in football karma and I think after years of Italian domination, and several finals lost by virtue of superior force in Europe that I mentioned before, this team has earned the statement, the victory. As Mourinho's Inter earned it."