Celtic have completed the signing of Thomas Gravesen from Real Madrid on a three-year contract.
The 30-year-old Denmark midfielder flew to Glasgow on Monday for talks and a medical before returning to the national team camp last night without signing a contract as reports emerged there were concerns about an old knee injury.
However, the Bank of Scotland Premier League champions and CIS Insurance Cup winners have now announced the former Everton player has joined them after they sold Stilian Petrov to Aston Villa.
Gravesen said: 'I am delighted to have joined Celtic, one of the biggest clubs in the world.'
Celtic also have the option of keeping the former Everton player for a further year.
The signing is a major coup for the Glasgow giants after losing Petrov to former boss, Martin O'Neill, who is now at Villa Park.
But the arrival of Gravesen, who is currently away on international duty, will enhance the Hoops' squad as they embark on a Champions League campaign, which sees them up against Manchester United, Benfica and FC Copenhagen.
Strachan and Celtic chief executive Peter Lawwell beat off interest from a number of English clubs, including Newcastle United.
Gravesen added: 'When I was made aware of Celtic's interest, naturally I was very keen to talk to the club and now having spoken to the manager, the chief executive and other people at the club I am very excited about this move.
'I am eager now to get going and do all I can for Celtic.'
Strachan has been looking for 'personality players' since the high-profile departures of Roy Keane, John Hartson and Chris Sutton this year.
And the arrival of Gravesen follows last week's signings of Jan Vennegoor of Hesselink and Lee Naylor.
The Dane is expected to be the last of their summer signings, but is keen to make an impact with the Hoops.
'I look forward to meeting up with my new team-mates next week,' said Gravesen, who faces competition from Neil Lennon, Jiri Jarosik, Shunsuke Nakamura, Stephen Pearson, Alan Thompson and Evander Sno for a place in midfield.
'The team did brilliantly last season to win the championship and together we will be trying to retain the title and do as well as we can in the Champions League.
'I know other Danish players who have had the opportunity play with Celtic and they have nothing but great things to say about the club.
'I have also visited Celtic Park for matches where the atmosphere is tremendous and I am very much looking forward to playing there.
'I am aware of Celtic's magnificent support and I will be doing all I can to bring as much success as possible to the club for the fans to enjoy.'