The Scottish champions, who used to keep their former training site at inadequate Barrowfield under wraps from signing targets like Pierre van Hooijdonk and Paolo Di Canio, say they now have a complex to rival the best in the world.
"Personally, it means that I can now wholly concentrate on just football," said Strachan, who along with captain Stephen McManus, chairman Brian Quinn and Celtic chief executive Peter Lawwell, was on hand yesterday to cut the green ribbon and declare the complex officially open.
"I loved training at Barrowfield, the surface was good but when I was there I got involved in business and football. I can switch my phone off here and just deal with football and so can the players."
The manager added: "We are proud of this, it is fantastic. I'm sure it will help [attract players]. At Aberdeen I trained in the local park and then when I went to Manchester United the training facilities were fantastic so I'm sure that will help. But the standard of your team and the possibility of winning things is important."
Lawwell, who dismissed speculation that Celtic were set to offer Strachan an improved contract as "nonsense", added his praise for the Lennoxtown project, but revealed that there are no plans to expand or refurbish Celtic Park.
"The training facility is fitting for a club of Celtic's stature," he said. "We are thrilled and very proud. It has been a long haul and we have created something very special so it is a great day for the club.
"There are no plans for the stadium at the moment. We are quite happy with the capacity and the facilities we have. Clearly the old stand would be the first priority but at the moment we have other uses for funds that are available."