This is the first Lions tour to South Africa since 1997 when McGeechan coached them to a 2-1 series win.
The highly-regarded Scot, who also toured South Africa as a player in 1974, is determined to achieve more success with the red-shirted tourists.
"The rugby is number one and certainly for someone like myself who came here first as a player and then as a coach," he told the assembled in Johannesburg.
"To come to a country where rugby has always been number one and so important, raises your own ambitions, because you know you're in an environment where it is important to everybody in the country.
"Of course it's a tough place to tour. I think we have to become part of South African rugby over the next seven weeks.
"We take it on board, we embrace it and we are part of it. I never knew any easy grounds and I don't anticipate any on this tour either."
The task of beating the World champions in their own back yard is one that clearly enthuses McGeechan, who said his South African counterpart Peter de Villiers will be 'pretty pleased' that a lot of his players are in good form.
He confirmed that the Leinster and Leicester Tigers players involved in the weekend's Heineken Cup final will not be considered for selection for the Royal XV game, meaning Brian O'Driscoll, Rob Kearney, Luke Fitzgerald and Jamie Heaslip will have some extra time to get up to speed on how the 2009 Lions operate.
McGeechan added: "We're delighted to be here now. It's always a relief when you arrive. We're here together now and everybody's fit.
"We watched the European Cup final together and it's good to have those players on board now and we're ready to go I think.
"Rustenburg is the start against the Royal XV and then we'll look to build from that.
"We'll look to give everyone a game in the first three matches. We'll play combinations.
"I've already said to the players that they'll all get an opportunity to play for a Test place. I don't anticipate picking the Test team until Test week.
"The Test team will probably have its first game together in the first Test, but we will obviously be working on combinations and see different players playing together.
"I think it's important that we can see the opportunities that they can be given and how they can bring different things.
"As coaches, we've got to keep an open mind for the first six games of the tour."