The cut-price food outlet is set to submit a planning application to Fylde Council within the next few months for the premium land on the corner of St George's Road and Clifton Drive North.
The German supermarket giant has bought the property, which was on the market for £1m earlier this year, and is now drawing up plans for a 16,000sq ft shopping centre on the site of the historic building.
Members were told about the sale of the building at an annual meeting on Thursday.
Officials at the club confirmed the building had been sold but would not go into further details.
It was unclear today where St Annes Conservative Club would be re-sited in the town.
While the Conservative Club is not a listed building, it is within the St Annes Conservation Area which means any new development would have to be in keeping with other buildings near its location.
Aldi is aiming to build a standard-sized store which would employ between 12 and 16 people and provide underground parking for up to 70 cars.
Officers will also be included above the store.
The company bought the former JobCentre and Blackpool and The Fylde College hair and beauty school building at the back of the Conservative Club last summer and that will form part of the scheme.
John McFarland, Aldi's property developer for the North West, said: "We are delighted we have managed to get this opportunity to open a store in St Annes."
Aldi already has two stores on the Fylde coast - at Waterloo Road in South Shore and Poulton Road, Fleetwood.