The Belgian international goalkeeper completed his move from Bari this week and was presented to the media.
"It is a great pleasure for me to be here," said the new signing. "I chose Bologna because they have such immense history behind them.
"Negotiations were brief and decisive. It took me only a minute to choose Bologna. I will give my motivation and great enthusiasm to the new project that is taking shape here."
Gillet has spent almost all his career in Italy, including 11 years at Bari, who were relegated this season.
With 12 years in the Peninsula at Monza, Treviso and Bari, he is the longest-serving foreign goalkeeper since World War II.
"It's an honour for me, especially considering the reputation of Italian 'keepers abroad. I love Italian football, as the level of competition is so high," continued the 32-year-old.
"The moment I arrived in Italy, I'd never have thought that I could stay in the same club for such a long time. Now the moment has come to change and I am convinced Bologna are the right choice.
"It's like a second career for me and I am very motivated, as I start from scratch and have to prove myself all over again.