The 22-year-old was born in the Isle of Man and had been with his boyhood club since the age of seven. He made 170 appearances for Celtic and has played 12 times for Scotland.
The defender completed a medical at London Colney on Thursday and will immediately join-up with his new team mates. He will wear the No 3 shirt.
Unai Emery said: “We’re delighted Kieran is joining us. He’s a very talented player who will continue to improve. He increases our options defensively and I look forward to him joining our group.”
Tierney told the club’s official website: “It feels great. I’m delighted to be here. Obviously I’m injured now, but I’m just looking forward to getting back on the pitch, training and getting involved with the squad.
When I was younger, [my ambition] was always Celtic. The ambition was Celtic and that was my dream when I was younger.
“I’ve done that, I’ve made my dream, I’ve lived my dream and I’ve loved every single minute of it. Now I just feel was the right time to take a step on. I feel this is a great opportunity for me.”
Tierney won five Scottish Premiership titles and made 40 appearances in all competitions for Celtic during the 2018/19 campaign.
He becomes Emery’s fifth signing of the summer window – joining Nicolas Pepe (Lyon), William Saliba (Saint-Etienne), Gabriel Martinelli (Ituano) and Dani Ceballos (Real Madrid, loan).