Silva, 28, looked set to join the Foxes on deadline day last summer as a replacement for Chelsea-bound Danny Drinkwater, but the paperwork from his transfer arrived 14 seconds late.
As a result, world football's governing body FIFA rejected Leicester's appeal to register Silva, leaving the midfielder in limbo.
However, the France-born playmaker has now been officially registered following the start of the January transfer window and he is looking forward to putting a difficult few months behind him.
Speaking to Leicester's club website, Silva said: “It’s been very frustrating, but now the difficult times are past me and now I’m very happy to be close to my goal.
“I’ve been working hard every day to arrive at this moment and I’m in good shape.
After the completion of his registration as a #lcfc player on New Year’s Day, here's what Adrien Silva had to say in an exclusive interview with LCFC TV https://t.co/SEwAZ9bLyI pic.twitter.com/gEvcMZ0sCX— Leicester City (@LCFC) January 1, 2018
“It’s been very important to keep training because it’s a long time not playing and of course I can work and train more than normal, but there is nothing better than the game.
“I will be in good shape because I have worked a lot – I have confidence in that – but I have to play games to get better.”
Silva was allowed to start training with his new team-mates in October last year and could take part in behind-closed-doors friendlies before any debut in the new year.
He could make his debut for Leicester against Huddersfield on New Year's Day after the club were given special dispensation by the Football Association.
Claude Puel's side only needed international clearance regarding Silva's move, which the FA has now given, because he has been registered since September.