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.
Both will go straight into Allen's squad for the Championship clash with Crystal Palace at Selhurst Park on Saturday as City attempt to bounce back from their opening-day home defeat by Blackpool.
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."