The 22-year-old Croat defender's move fell through late on deadline day.
"It is not true that I have not passed [a] medical," he said on Twitter.
"Everything was perfect, I am completely healthy and fit. Transfer was not realised because Torino at the last minute wanted to change the initial agreement with Celtic."
Simunovic joined Celtic from Dinamo Zagreb exactly a year ago but made the last of his 18 appearances in January, when he suffered a knee injury against St Johnstone.
Some reports claimed that Torino had reservations following medical checks after Simunovic travelled to Italy.
But the player refuted those accounts and said he was speaking out because, "most important of all", he wanted to stress that he remains committed to Celtic.
He must now fight for his place in Brendan Rodgers' side with fellow central defenders Kolo Toure, Eoghan O'Connell, Erik Sviatchenko and Efe Ambrose.
"I prefer to talk only on the field, but this time I want to say something to the Celtic fans who have always supported me and as a player it means a lot to me," said Simunovic.
"My head is in Celtic and I am 100% focused on the field and the challenges ahead.
"I am fit, I train with the team and, of course, the coach decides when I will start to play.
"And, when I start, I can promise one thing. I'm going to give more than maximum for Celtic.
"Behind me is 'turbulent' period, starting from injury until transfer to Turin."
Celtic's only deadline-day business was to loan right-back Saidy Janko to Barnsley for the season.
Simunovic's fellow central defender, Ambrose, rejected a transfer to Belgian top-flight club Standard Liege after a fee was agreed between the clubs.
Jozo Simunovic says his proposed transfer from Celtic to Torino collapsed because the Serie A club changed their offer at the last minute.