Team boss Christian Horner said Lambiase, who reports to technical director Pierre Wache, will also remain in his role with triple world champion Verstappen next season.
Wheatley's duties will be split, with Steve Knowles becoming head of sporting regulations and Richard Wolverson in charge of race team operations.
Red Bull have lost a number of senior employees, including star designer Adrian Newey who is joining Aston Martin next March.
"Jonathan moving on to take up a new challenge at Audi (Sauber) has actually provided a great opportunity to just reorganise how we go racing," Horner told motorsport.com.
"It’s a step up for everyone. It’s a very strong front manoeuvre."
The champions are 20 points behind McLaren in the constructors' standings with seven rounds remaining, including Singapore this weekend.
