Kayal has been in negotiations with the club for a number of months after looking to improve his terms following an impressive debut season.
The Israel midfielder was linked with moves to the likes of Manchester United and Liverpool after his return from a hernia operation on Boxing Day last year heralded Celtic's best spell of the season.
But he fractured his wrist in the 3-2 defeat by Inverness that ultimately cost Celtic the SPL title in May and missed the Scottish Cup final win over Motherwell.
He has struggled to regain that form this term, like many in Neil Lennon's team, but he feels a run of fitness will help him do so, especially now the distraction of contract talks are out of the way.
Kayal said: "I'm very happy to have signed a new contract. I just want to work hard and focus on my football.
"I want to stay here a lot of years. When I came here I was happy to sign for a big club, now I'm very, very happy.
"There were a lot of rumours last summer but I'm happy to stay here.
"I never said I wanted to leave. I like the club and the people and the fans are important. They give me energy to give everything.
"The manager wanted me here. There were a lot of rumours but I never thought for one moment about leaving the club."
Kayal insisted he knew nothing about any concrete interest in his services.
"I don't know anything about that, it was just rumours," he said."
Celtic moved towards giving Kayal a wage rise to reflect his importance to the team and head off any possibility of the player leaving.
"The gaffer, the people in the club, spoke to me in April and May," he said.
"I said before the season was finished that I wanted to stay and sign a new contract.
"It took a long time because there were a lot of breaks for international football, I was injured two or three times, I broke my nose, and the deal took a long time.
"But I'm very happy now that the deal is done and I can just focus on football.
"It's very important for me to clear my mind and just focus on football because when I go outside the club people ask me about the contract.
"Everyone saw the rumours and people ask me whether I'm leaving or not.
"I always just want to concentrate on football and enjoy my job and I want to do that now. It's better for me to do that when I'm happy and can just focus on my job.
"I feel myself and I know what I can do when I play. At the moment I don't play the same every game.
"But I have had a lot of injuries, I feel unlucky. I went to the national team twice and came back injured and broke my nose in Australia, and broke my wrist before the end of last season.
"It's not easy. Sometimes I go down but I'm strong and I want to come back and play for the club and the manager.
"The manager always believes in my talent."
Celtic face Rennes in the Europa League in France on Thursday looking for a much-needed win, having only tasted victory in four of their last 12 games.
Kayal is looking to put his disappointing weekend behind him - he was substituted at half-time with Celtic three goals down at Kilmarnock after risking a second yellow card in a flashpoint late in the half.
"I felt angry in the game and took a yellow card," the 23-year-old said.
"The gaffer thought about the team and changed me. I was very happy because the team came back and everyone did their job well.
"The most important thing is to think about the next game and to win.
"There are a lot of games to go but we must start winning games and just focus on the next one."