The 82-year-old Soho dining room, which used to be owned by Marco Pierre White, is undergoing a makeover after being bought by brothers Sam and Eddie Hart.
They are investing about £2.5million in restoring Quo Vadis as a glamorous art deco grill room.
Sam Hart said the tap water would be passed through a filtration system that would also carbonate it for customers who ordered sparkling water.
The water would be served in a "really smart, stylish bottle" more in keeping with the new surroundings than a jug, accompanied by bread and olives.
There would be no limit on how much water customers could ask for but there would be a cover charge of around £1.50 to £2 per head for the cost of the bottles and the filtration system.
Hart said: "It is completely green, it looks nice and tastes good - and all for a smaller charge than bottled water."
The Harts, who also own Spanish restaurants Fino and Barrafina, hope to recreate the great grill tradition largely lost when the Savoy and the Connaught hotels closed their grills.