Strachan said the move for Guzan did not mean number one Artur Boruc, who signed a new deal this month, was poised to leave the club.
"I'm thinking about Brad as an investment for the future. If you get someone who could be good value for years then you do it," said Strachan.
Guzan arrived at Celtic Park after starring for his country in a 2-0 friendly win over Sweden.