Hamer made 37 appearances for Charlton Athletic this season but has left The Valley with his contract set to expire July 1.
The 26-year-old has signed a four-year deal at Leicester and revealed that the challenge of testing himself in England's top flight was behind his move.
"It's fantastic to be here," Hamer told Leicester's official website.
"It was an opportunity that was too good to turn down for me and I'm looking forward to coming on board and improving myself as a player.
"Being involved in Premier League football has always been a dream of mine since I was a kid.
"It's been a long road and to finally get the opportunity to do that was a big factor in the move.
"I want to challenge myself in my career and coming here to a big club going into the Premier League is a big opportunity for me."
Hamer came through Reading's youth academy and spent a number of spells on loan at Brentford in addition to stints at Crawley Town and Exeter City.
He signed for Charlton in 2011 and went on to make 121 appearances in all competitions for the club.
His arrival places further doubt on the future of Leicester goalkeeper Kasper Schmeichel.
The Denmark international – an ever-present in the club's Championship-winning campaign – is out of contract in the close-season.
Reports emerged that the former Manchester City and Leeds United man was set to sign an extension earlier this week but nothing has been announced by the club.
