She said: "We have had improvements already, but we are expecting visible changes in availability as the depot is now up to full productivity. This will mean our regional distribution centres can focus more on faster moving lines."
The Coventry site will service 3,300 Co-op food stores and will employ 670 staff.
Co-op chief executive Martin Beaumont said: "We now have a much more effective and efficient supply chain, enabling us to negotiate significantly better terms with our suppliers, which is an ongoing priority for us."
The group has also tried to minimise the environmental impact of the centre, which is powered by 100% green electricity.
Trevor Ashworth, director of Co-op's food retail logistics, said: "Having one national centre, in such a central location, is more efficient and reduces the number of journeys vehicles have to make to deliver to us. It also reduces the number of journeys we need to make to deliver to our stores."