Now a question must be answered. Are they capable of replacing those players who have left?
It will not be easy filling the boots of Gary Hooper, Victor Wanyama and Kelvin Wilson in the Champions League group stage.
It will be hard for somebody to take over from Hooper in particular as the striker scored so many goals, both at home and abroad, for Celtic.
But Neil has brought in the Finnish striker Teemu Pukki from German club Schalke for £3million. He also has Amido Balde. Then there is Anthony Stokes.
I feel Stokes could rise to the challenge of replacing Hooper and become the Scottish champions' main goalscorer domestically and in Europe this season.
He certainly seems to be doing that already. He is playing to a very good level. He set up James Forrest to score the winning goal for Celtic against Shakhter Karagandy.
The Irishman spent much of last season out injured. He came back towards the end of the season and had an exceptional game against Hibs in the Scottish Cup final. In many ways, he is like a new signing for Neil.
I think the capture of Pukki hinged on Celtic qualifying for the Champions League group stage. Once they had secured their spot they had the funds to finance his transfer.
The chance to join the continent's elite in that competition probably helped to convince the player, who was playing at a high standard in the Bundesliga, that coming to Scotland was the right move.
The Champions League is a big carrot for a player. I am sure the prospect of playing against AC Milan, Ajax and Barcelona will have been attractive to him.
I think Pukki will score goals. He has played at a very high level in Germany and has done well and I am sure he will thrive in this country and in European competition.
Neil has signed Nir Biton in midfield, and he has also brought in replacements defensively. He has added the Dutch defender Virgil van Dijk and the French stopper Steven Mouyokolo to his squad.
Time will tell if these lads are capable of doing a decent job for Celtic. But they certainly provide cover at the back.
Wilson performed far better last season. But I am hopeful that the defence will continue to function in his absence with Efe Ambrose, Van Dijk, Mouyokolo and Charlie Mulgrew all on the books.
Scott Brown has started to play one in instead of out wide and is becoming increasingly influential in midfield. I think the captain can help to ease the pain of Wanyama's loss given how well he is performing.
I think Neil had to be careful not to disrupt the harmony within his squad with his new signings. The spirt he has helped to foster within the camp played a huge part in the success his team has enjoyed.
You could see how tight the group is with the way the players and the coaching staff reacted when Forrest scored his dramatic late winner against Karagandy last week. Neil ran the entire length of the touchline to join in with the wild celebrations.
If he altered the set-up too much and if he brought in players who would break the wage structure then it could have jeopardised that togetherness. Sometimes, if a player comes in on far better money it can become an issue.
Of course, Celtic work to a financial template. They cannot afford to offer players the wages that clubs in England or in Europe do.They have to live within their means and they have done so very successfully.
Some people would like to see them change their signing policy. But I think it would be foolish to break up a successful strategy.