Team principal Bruno Famin made the call shortly after the Monaco Grand Prix where Pierre Gasly picked up just the team's second point of the season in a race where Esteban Ocon failed to take part in the restart having collided with his team-mate on the red flagged first lap.
White was a key part of the engine project that helped bring Renault (Alpine's parent company) and Fernando Alonso title success in 2005 and 2006 and his exit was confirmed at the Enstone factory on Wednesday.
The 58-year-old is highly respected in the F1 paddock and leaves his role as director of operations - a position he has held at the team factory since 2016.
While had joined Renault in 2004 as a managing director and is the latest key figure to depart a team who have been in a state of management flux for many months now.
Big names have left Alpine
Former team principal Otmar Szanfauer and another title winning star in Alan Permane were the first big names to depart under Famin's watch during the middle of the Belgian Grand Prix weekend last summer.
But as improvements failed to materialise this year, technical director Matt Harman was also dismissed as was head of aerodynamics Dirk de Beer.
Well renowned designer Bob Bell then joined Aston Martin, although Alpine recruited former Ferrari and McLaren engineer David Sanchez earlier in May.
An Alpine spokesperson has said: "As part of the team's wider operational restructure, we can confirm the departure of Rob White.
"The team is thankful for Rob's efforts during his long career both at Enstone and at Viry-Chatillon, where he led the championship-winning engine project in 2005 and 2006. We wish him the best in his future endeavours."