The societies said that they would seek support for a merger from their combined 175,000 members in meetings due to take place in July and August.
If approved, the merger would create the fourth-largest co-operative in the UK, with a turnover of £500m and more than 350 stores.
The societies said they would retain both their HQs in Oxford and Walsall but there was no guarantee that jobs would not be affected. OS&G employs more than 4,000 staff, while West Midlands employs 2,200.
OS&G Co-op’s chief executive, Bob Burlton, will lead the new society until he steps down next year. Following the merger, Ben Reid of West Midlands Co-op will be appointed chief executive designate and will succeed Burlton as chief executive.
OS&G president Vivian Woodell said: “We are convinced that the combined society will be more profitable and hence stronger than if we remain apart.”