The 23-year-old put pen to paper on his £2.4million switch from German giants Schalke on Friday night, but did not feature at Tannadice on Saturday as Neil Lennon's side claimed a 1-0 win over Dundee United.
Celtic faced a lengthy battle for Pukki's services, but finally landed their man just hours before the transfer window shut as he agreed a four-year deal at Parkhead.
Boss Lennon has likened the Finnish star to recently-departed Hoops striker Gary Hooper, and former Hibs and Kilmarnock gaffer Paatelainen is confident the 24-times capped forward can star in the Scottish Premiership.
He said: "I think it was a really good move. I believe that the games will be completely different to Schalke.
"Game time is the most important thing for Teemu right now. Teemu is a talented player, but every player needs responsibility and playing time to develop. Game time is, in my opinion, more likely now.
"The Scottish league is a good league. It is not the top league, but it is a good league though. "Celtic, on the other hand, are one of Europe's top clubs. It is a great, big club, who take good care of their players and the fans are superb.
"This transfer will allow Teemu to play for championships and other trophies. Also, Celtic are once again involved in the Champions League. Sure, Schalke would have been, but now it is more likely that Teemu will play in these great competitions on the pitch."
Pukki will have to wait until the trip to face Hearts Tynecastle after the international break to make his Hoops bow as he bids to make a flying start to life in Glasgow.
Lennon's side will kick off their Champions League group stage campaign against AC Milan just days later and the striker is determined to make an impact on the Euro stage.
He said: "I was at home watching the draw on the internet and I was quite nervous and, in the end, I was a fan of Celtic.
"Last year I already played there with Schalke and now I hope I can help Celtic to go through. It's not an easy group as all the teams are quite hard.
"It will be difficult but, of course, we have a chance and Celtic already have shown last year that they can beat teams like Barcelona, so it will be a nice group.
"The players here always want to win and I think here we have a good chance of winning the championship and the cups, but we will have to work hard for them."
Celtic's opening Champions League opponents Milan were last night poised to complete the signing of former Rossoneri favourite Kaka.
The 31-year-old Brazilian midfielder came to prominence in his spell with the Italians but has fallen out of the picture in Spain.