Austrian Lauda was named as non-executive chairman of the British-based team's board when 2008 champion Hamilton was signed from McLaren last September.
Since then, Mercedes have announced the departure of motorsport chief Norbert Haug after more than 20 years in the high-profile job.
Lauda, 63 and a former Jaguar team principal, is expected to play a link role between the team and Stuttgart car manufacturer.
The Austrian retired from Formula One racing in 1985 to focus on his aviation interests. The low-cost Niki airline he founded in 2003 is now owned by Air Berlin after Lauda sold his stake in 2011.
Air Berlin thanked Lauda in a statement for his "committed, stimulating work for the benefit of the company".
Mercedes finished last season a disappointing fifth overall, with Hamilton joining this year in place of the now-retired seven-times champion Michael Schumacher.
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