Villa confirmed that the winger would not be offered a new contract earlier this week, leaving him available to the newly-promoted Foxes on a free transfer.
The 24-year-old told his current club's website: "I'm absolutely thrilled to be joining. Everything about Leicester City is moving forward at the moment and it's going to be a great football club to be a part of.
"It was a great 16 years for me at Villa and I had some really wonderful times there that will stay with me forever. I'm coming away now with my head held high and really looking forward to this fresh challenge with Leicester. I just can't wait to get going.
"I've watched some of Leicester's games over the last season and the lads have really played some great football. It's incredible what they have achieved, and they've deserved every bit of their success."
Albrighton's contract with Villa will expire on July 1.