The Hoops need only a work permit to complete the transfer of Israeli midfielder, Nir Biton, from FC Ashdod.
And Schalke's striker, Teemu Pukki, will arrive right behind the 21-year-old, if personal terms can be agreed.
Neil Lennon's side have agreed a transfer fee with the Bundesliga club for the Finn, and the deal is expected to be completed before the transfer deadline, which is midnight on Saturday.
Biton was at Parkhead last night to watch his new team-mates defeat Shakhter Karagandy 3-0 and seal their place in Pot 4 of the draw.
But, astonishingly, Celtic are quoted at 4-1 to emulate last season's achievement in reaching the last 16 - even before they know who they will be facing.
Lennon does not care which names are drawn out alongside Celtic's because he believes his players have worked a miracle to get this far.
There was no hint of celebration as Lennon said: "We played very, very well under the greatest pressure I have ever felt in my life.
"I am spent at the minute.
"I have been seven weeks preparing for this, but the best-laid plans sometimes go to waste.
"Losing three magnificent players for the club, and not being able to replace them, makes last night even more remarkable.
"It's the best achievement of my career, under the circumstances with all the preparation we have tried to do, the things that have gone wrong, injuries piling up, and losing players, particularly Kelvin Wilson when I didn't envisage that happening.
"Then, to come from two goals down ... I always maintained we deserved something from the first leg - and I was proved right last night.
"They were heroes, and I can't speak highly enough of them.
"It is all about the players, and my backroom staff, because they are the ones who have done all the work."
James Forrest was the injury-time hero with the vital third goal to add to strikes from Kris Commons and Gerogios Samaras either side of half-time.
The youngster was an injury doubt before the tie, and was indicating he needed to come off after taking a very heavy tackle in the dying minutes.
"He was unbelievable," said Lennon. "We were going to make a substitution just before he scored, then Anthony Stokes produced a fabulous piece of skill and, at the end of it, picked out James with the right pass."
Lennon always retained faith his players could turn the tie around - even though he sensed many others did not.
He said: "I have been really disappointed from the reaction to the first game in Kazakhstan, even from sections of our support.
"So, I think there are a lot of people who owe our players an apology.
"These players have been performing miracles for the last year-and-a-half, and they performed an even bigger one last night.
"They should be feted for it. But, the first time they have a bad game or bad performance, the phone-ins and internet are full of negativity.
"It makes my job impossible at times.
"But, being in this draw today is the best feeling in the world, though it hasn't really sunk in yet because I have been so angry all week.
"I am fed up of the negativity which surrounds the Scottish game and fed up of people trying to hammer players who are doing their best to be successful.
"It does wear you down.
"That's five qualifying and play-off rounds we have come through in the last two seasons, and no one has any idea how pressurised that is.
"And, with the climate the way it is, there's more pressure on the team to get there because everyone is saying in Scotland it is Armagedon.
"I don't know what they have brought in, it must be £50m, and we haven't had a hand.
"There has been no spending really, and we could have been doing with it.
"Nir Biton was here last night, and work permit permitting, that deal should get done.
"We're hoping Pukki will come, too. That's been agreed with the club, and it's just the player's finances now.
"But they will have to play well to get into that team."