The winger was previously on loan at Raith Rovers last year and made 19 appearances for the Stark’s Park club as they secured a Championship promotion play-off spot.
However, boss McGlynn confirmed he is set to be out for a 4-8 week spell after picking up a hernia-related injury.
“I am delighted to be here and to have the move all sealed after a couple of weeks of going back and forth,” he said of his move to the Bairns.
“It’s such a big club and we want to get promoted and I really believe in that goal.
“For me personally, it has been a hard few months with what has been probably my longest injury since I started playing football professionally.
“I’ve been working so hard to get back and I just can’t wait to be playing.
“It will be great to link up with the gaffer again too. It was a big factor.
“I had a great time at Raith Rovers and I really enjoyed the training and the way the team played.
“Everything they did was enjoyable and when I got a phone call to come here, I was excited about it.
“It is a big year for myself and I need to push on. I want to really get through the next few months as well as I can and see where it takes me.”
He also believes that his style of play will suit the way Falkirk want to play this campaign under the ex-Raith Rovers boss.
Kennedy added: “I am a really positive player and I want to take a man on. My first thought is to go forward.
“Goals and assists are what I need to add to my game and I came here to change that.
“I want this club to be at the top of the table and I want to help them lift the title.”
Manager McGlynn also shared his excitement at linking up again with the Ibrox youngster, saying: “Kai is a player Paul Smith and I have worked with previously.
"We enjoyed working with him and he enjoyed working with us, and we hope that will be the same again. Kai gives us real competition in the wider areas, he can play at both sides and in a number ten position.
“He’s going to be in competition with the guys who are already in the team, and he needs to force himself in which is exactly what he’s going to try and do.
"It will breed good competition with others trying to play well to stay in the team.”