The 24-year-old started his career at Aston Villa, but will end his long stay at the club once his contract expires on July 1.
Foxes boss Nigel Pearson impressed Albrighton with his ambitious plans for the future after steering his side back to the Premier League.
"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," the new signing told Villa's official website.
"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 spoken to the manager and I know he has big plans, so I just can't wait to get started and be involved. Before I joined I spoke to a few people and nobody had a bad word to say about the manager or the club, so I'm delighted to have everything agreed for the new season.
"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.
"Now I'm looking forward to getting involved myself. I'm a direct player who is very positive with the ball and who likes to cross. All strikers say they like crosses in the box, and they can guarantee that I'll be doing that for them."
Albrighton becomes Leicester's second signing of the day as the club also confirmed that defender Matthew Upson will join from Brighton.
Albrighton's agent, Tim Webb, reported that there had been considerable interest in the player from several Premier League clubs following his departure from Aston Villa.
And the winger has opted to link up with Leicester, who amassed 102 points in clinching the Championship title.