Clarke, 27, has moved to the Walkers Stadium on a three-month loan while Hungary goalkeeper Fulop, 24, will stay with the Foxes until the end of the season.
Allen said: "Clive has experience, a great appetite and hunger to play and has come here for three months to prove he is good enough. At other clubs he has been picked as their captain and I believe he will be a good acquisition for us.
"I am delighted Marton Fulop has agreed to join us on loan for the season. He has great presence, a great attitude to work and to improve and is a goalkeeper I've tried on many occasions in the past to get on loan.
"I believe this is a significant signing for Leicester City."