The side to face the Springboks at the newly renamed ABSA Stadium includes six Welshmen, five Irishmen and four Englishmen, with a further three Welshmen, three Irishmen and one Englishman named on the replacements bench.
Ireland's Paul O'Connell captains the side from the second row, where he is joined by Wales international Alun-Wyn Jones.
Elsewhere up front, previous Lions Test players Gethin Jenkins and Phil Vickery are selected at prop, with Lee Mears packing down between them in the front row.
Leicester's Tom Croft, who missed out on selection for the original 37-man Lions squad back in April, is named at blindside flanker, with Irish duo David Wallace and Jamie Heaslip at openside and No8 respectively.
Mike Phillips and Stephen Jones form a Welsh half-back partnership, with 2005 Lions skipper Brian O'Driscoll selected outside Cardiff Blues star Jamie Roberts in the centres.
Ospreys team-mates Lee Byrne and Tommy Bowe start at full back and on the right wing, with Ugo Monye of Harlequins and England winning the race for the left-wing berth.
As for the replacements, Welshmen Matthew Rees and Adam Jones provide front row back up, while Donncha O'Callaghan is the second row option and Martyn Williams covers the back row.
Harry Ellis and Ronan O'Gara provide options at halfback and Leinster's Rob Kearney has recovered from the dead leg he suffered against Western Province to claim the final place in the 22.
"The Test team has been picked on form following the six provincial matches," said McGeechan, who masterminded the most-recent series winning Lions tour back in 1997.
"There were some very difficult calls to make as the players as a group and individually have done everything that we have asked of them and performed on the field.
"The preparation for the First Test has been very positive. It has been a challenge to reach the First Test with an unbeaten record as we have played a variety of provincial teams across the country.
"This challenge is a unique one in the modern rugby calendar in that it comes only in a Lions context these days. The players have had to adapt to preparing and playing more frequently. They have answered that challenge.
"It has been 20 years since a Lions team has won all of its' provincial matches leading up to the Test series so it is very satisfying to be in such a position. The entire squad and the management have worked hard to create an outstanding team environment. Everyone has done this very professionally and it is fair to say that I would not change anything that we have done so far."
"Playing South Africa on its home soil is one of the ultimate challenges for the British & Irish Lions," added Davies, who was a victorious Lion in New Zealand 38 years ago.
"South Africa also happen to be world champions which adds an extra edge to the series, just as it did in 1997.
"The tradition between the Lions and the Springboks is legendary and after the six lead up provincial matches the rugby world is waiting with great anticipation for the First Test in Durban this Saturday."
Lions (vs South Africa, first Test, Saturday June 20)
15. Lee Byrne (Ospreys/Wales)
14. Tommy Bowe (Ospreys/Ireland)
13. Brian O'Driscoll (Leinster/Ireland)
12. Jamie Roberts (Cardiff Blues/Wales)
11. Ugo Monye (Harlequins/England)
10. Stephen Jones (Scarlets/Wales)
9. Mike Phillips (Ospreys/Wales)
8. Jamie Heaslip (Leinster/Ireland)
7. David Wallace (Munster/Ireland)
6. Tom Croft (Leicester Tigers/England)
5. Paul O'Connell (Munster/Ireland) Captain
4. Alun-Wyn Jones (Ospreys/Wales)
3. Phil Vickery (London Wasps/England)
2. Lee Mears (Bath/England)
1. Gethin Jenkins (Cardiff Blues/Wales)
16. Matthew Rees (Scarlets/Wales)
17. Adam Jones (Ospreys/Wales)
18. Donncha O'Callaghan (Munster/Ireland)
19. Martyn Williams (Cardiff Blues/Wales)
20. Harry Ellis (Leicester Tigers/England)
21. Ronan O'Gara (Munster/Ireland)
22. Rob Kearney (Leinster/Ireland)