Bhoys boss Neil Lennon confirmed over the weekend that the man who has managed Finland, South Africa and a host of clubs had agreed to accept the advisory role.
Baxter, 56, watched the Parkhead men in action against Lyon and Arsenal at the Emirates Stadium on Saturday and Sunday respectively and spoke to Lennon and his management team.
He is delighted that, after long negotiations to persuade the Finnish FA to allow him to remain their national team manager and help Celtic, the deal has been given the green light.
"It is not going to be the official connection that I think we would have liked it to be," Baxter told the Evening Times.
"The Finnish FA were very keen to distance themselves from that one.
"But the connection has been made between myself and Celtic. I am in contact with them as a consultant, in inverted commas.
"What we have tried to do is find a happy medium, so that I can be in a position to help out Celtic but also do it with the blessing of the Finnish FA.
"They have to be able to see some value in it for them, and the way that everything came out at first and emerged through the media, they felt as though they were the ones losing out.
"I have to respect that because, obviously, the European Championships is now my most important task.
"If I can find a balance that allows me to do that while also being available for Celtic, then everyone is happy."