Move comes as Tussauds takes over and new South Bank lease is signed for 25 years.
Architect Marks Barfield has sold its one-third stake in the London Eye to Tussauds, just a day after the museum operator bought out British Airway's 33% stake for £100m.
David Marks said: "British Airways' decision to do a deal direct with Tussauds left us with some pretty stark choices. In the final analysis, the best solution was to reach a settlement with Tussauds, which we have done."
"This arrangement means that we will no longer be involved in the Eye on a day-to-day basis. However, it maintains our involvement with the company - as the originators, founders and architects - and allows Tussauds a greater say over how the company is run. As in the Chinese proverb, we have decided to embrace what we cannot avoid."
Marks Barfield's decision came as British Airways London Eye, the company which runs the attraction, signed a new 25-year lease with the South Bank Centre.
As in the Chinese proverb, we have decided to embrace what we cannot avoid
The agreement will be worth a percentage of turnover, with a minimum of £500,000 per year.
David Sharpe, managing director, British Airways London Eye, said: "I am delighted that the British Airways London Eye will now be preserved on its current site for the enjoyment of generations of Londoners and visitors for many years to come. Our iconic British landmark can now look forward to a long and prosperous future."