McGeechan has been at the Wasps helm for four years, during which time he led the side to an array of silverware including both the Guinness Premiership and Heineken Cup titles.
"After discussions in partnership with London Wasps, I can confirm that I will step down from my position as director of rugby," said McGeechan, who is about to embark on his fifth Lions tour as a coach or an assistant coach.
"This decision has been part of an ongoing dialogue with the Club, which began in January 2009 with executive chairman Mark Rigby, when I informed him that one of the options I was considering was to finish as director of rugby at the end of the season.
"I did this because I believe succession, planning and stability are very important and have been a key component in Wasps' success."
McGeechan has combined his role at Wasps with his current position with the Lions this season and now turns his attention solely towards the 10-match tour of the Republic which begins in just over a fortnight's time.
The 62-year-old has been a huge hit with both the players and supporters during his time with Wasps and he admits he could still be involved in some shape or form during the 2009/10 season.
"I have had four incredible years at Wasps and developed many special and significant friendships with fellow coaches and players and I am proud of the Club's achievements in winning three major trophies during that time.
"I am currently discussing with the Club the format of my involvement next year as the Board, quite rightly, has to be happy that a successful transition takes place.
"I would like to wish my successor, as well as everyone else at the Club, all the very best for the future.
"Wasps and its people will always remain very close to my heart."
Rigby confirmed that McGeechan has been involved in the process of searching for his replacement and that supporters can expect an announcement in the near future.
"We thank Geech for his massive contribution to the Club over the last four years, helping us to secure an impressive collection of silverware. He leaves the role with our best wishes and enormous thanks and he will be remembered as a key member of the Wasps coaching dynasty.
"As he prepares to travel to South Africa for the Lions tour we wish him the very best of luck with the series.
"Today's announcement marks the start of the next chapter in our history and it is with Geech's backing, contribution and input throughout the season, that we will look to confirm a new Director of Rugby shortly."