Schmeichel, 37, started his career at Manchester City and had spells with Notts County and Leeds before joining Leicester in 2011.
While with the Foxes, Schmeichel went on to win the 2016 Premier League title and also the FA Cup in 2021, when current Celtic boss Brendan Rodgers was manager.
Schmeichel – who left for Nice in 2023 and spent last season at Anderlecht – has 105 international caps and played against England in the group stages of Euro 2024.
"Celtic is one of the world's proper football clubs, a massive name and a place of real passion and success. Celtic is what football is all about," said Schmeichel, who is set to join his new club on their pre-season tour in the United States.
"I know Brendan very well, too. He is a top manager and someone I can't wait to work with again.
"I'm really looking forward to meeting up with the boys in America and start our work and then, of course, meet our fans who bring so much to Celtic.
"I will be doing all I can to keep Celtic on top and bring these brilliant supporters more and more success.
Rodgers feels Schmeichel will bring a positive mindset to the squad.
"Kasper is a real quality keeper and someone with the ability and personality to be great for us," he told the Celtic website.
"He is a guy I trust and someone who knows how to win. He lives for football and he is coming to a club where he will feel the same passion that he has for the game.
"I know he will feel right at home at Celtic and we look forward to working with him as we all aim for more success."
Newcastle manager Eddie Howe has confirmed that Alexander Isak's absence from the squad in Saturday's 4-0 preseason defeat to Celtic was a direct result of ongoing transfer speculation surrounding the striker.
Ibrahim Said has signed a two-year deal with Scottish Premier League side Motherwell.
Bayern Munich defender Alphonso Davies credited his crucial last-minute goal, which helped Bayern secure a 3-2 aggregate win over Celtic and advance to the Champions League Round of 16, to "instinct."
Bayern Munich defender Alphonso Davies netted a dramatic last-minute equalizer against Celtic in their playoff on Tuesday, securing a 1-1 draw and sending them through to the Champions League Round of 16 with a 3-2 aggregate score.
