The 26-year-old Ivorian was a free agent after leaving Tranmere for whom he made almost 150 appearances and scored five goals.
Foxes manager Nigel Pearson told the club website: "A number of clubs were interested in signing Zoumana this summer and we were one of those that had been monitoring him for a considerable period of time.
"I'm really pleased he's chosen Leicester City. It's important to us that we recruit players, not only with ability, but also with a desire to play for and work hard for this Football Club.
"He's a good player with a great attitude and I'm sure he'll fit in well with the current squad we have."
Bakayogo said: "This is a big club and a big challenge for me, stepping up into the Championship. I've taken the chance, I hope to have a good season this year and do well for the team.
"The Championship is a new league for me so I will have to work hard to catch up to the pace, but I'm looking forward to working with everyone."