The 23-year-old has joined the Scottish champions on a four-year contract, after Celtic reached an agreement with United on Monday.
Ciftci will wear the No 7 shirt made famous by Celtic icons Jimmy Johnstone and Henrik Larsson but insists he will not let the burden of that honour weigh him down.
“It’s a favourite number for myself too – I’ve been wearing it everywhere else I’ve been,” Ciftci said.
“But I know what it means to this club and the players who have worn it before, so it will be a pleasure for me to wear it here as well.”
Ciftci had one-year remaining on his deal at Tannadice and informed United he would leave at the end of his contract.
And after accepting an offer of £1.5m from Wigan, United granted permission to Celtic to open talks with the former NAC Breda forward.
“Celtic was always my first choice,” Ciftci said.
“Everybody knows how big a club it is. I knew it before I even came to Scotland. I’ve played two years against them now but you really see it once you sign for them.
“Hopefully I can bring a lot to the team. I’m fit to play, so it’s up to the manager if I play or not.
“I had two great seasons at United and I’m really thankful for that. Everyone at the club – the staff, the fans, my team-mates – they made we really welcome.
“It’s obviously really tough to leave a club like that after two beautiful seasons but I’m looking forward to a new chapter.
“I respected what Dundee United were looking for from the offers but it wasn’t something I was really thinking about at the time.
“I was training with United and was fully concentrated on getting fit. If it was going to happen, it would. I’m just happy it did.
“Hopefully we can get into the Champions League – that’s the biggest stage and where Celtic belong. I want a taste of that.
“You get a lot of pressure put on you here and it’s nice to have that. You will always be remembered here, especially if you do well – and I’m here to do well and be remembered for doing my best.”
Ciftci becomes the third player to leave United for Celtic Park this year, following Gary Mackay-Steven and Stuart Armstrong, who both joined the Hoops in January.
The Turkish forward, who scored 33 goals in two seasons at United, will be eligible to play for Celtic in their Champions League qualifiers against Stjarnan.
Celtic have already signed defenders Dedryck Boyata and Saidy Janko, as well as goalkeeper Logan Bailly this summer.