The Scottish champions have been after goal-scorer Ciftci for some time now and had two previous offers turned down. But a third offer has been successful, with United having been holding out for around £1.5million ($2.3m, 2.1m euros) for a player who has a year left on his contract.
Ciftci, who joined United for free two years ago and had also been approached by English side Wigan Athletic, will now discuss personal terms with Celtic.
A statement on www.dufc.co read: "Dundee United today confirmed that an undisclosed fee had been agreed with Celtic for Nadir Ciftci and permission has been granted for the Glasgow club to speak to the player."
The 23-year-old must be registered by Saturday if he is to be available for the Hoops' Champions League second qualifying round, first leg against Icelandic side Stjarnan FC next Wednesday.
Celtic's interest in Cifti comes despite the threat of a lengthy ban hanging over the striker. He faces a Scottish Football Association disciplinary hearing on July 20 over allegations that he bit Dundee midfielder Jim McAlister in the final game of last season.
Bailly is expected to complete his move from newly-promoted Belgian top-flight side Leuven, who announced on their website on Monday that Bailly had agreed a deal in principle to move to Glasgow for a transfer fee.
The 29-year-old won eight caps for Belgium, all in 2009 and 2010, and has also played for Genk, Borussia Moenchengladbach and Neuchatel Xamax.
The 6ft 2in (1.88m) goalkeeper comes in as cover for Craig Gordon following the summer departure of Lukasz Zaluska.