The deal, which is due to complete today, sees BAM remain at the site along with other tenants Goodrich, Arcellor Mittal and E-tech.
IM, which is owned by Lord Edmiston, said it would now look to alter the existing planning consent to attract more occupiers seeking larger floorplates.
Fore Business Park is in Stratford Road, next to junction 4 of the M42, and has 66,000 sq ft of existing office accommodation in two BREEAM 'Excellent' buildings which were speculatively developed in 2009 and currently at 85 per cent occupancy.
The site includes six acres of development land, with planning consent secured for two more office buildings totalling an additional 90,000 sq ft.
The acquisition adds to IM's portfolio of sites which includes Birch Coppice in Dordon, One Kings Court in Worcester and Solihull Business Park which will soon be home to the first John Lewis customer fulfilment centre.
It also acquired the Mell Square shopping centre in Solihull town centre last year.
Investment director John Hammond said: "Fore Business Park offered us two high quality buildings with existing income streams from four very good tenants, with the majority of leases extending over 10 years.
"The M42 market has witnessed a dramatic turnaround in recent months, exhibiting a strong demand that has left little stock for tenants to consider, particularly in good quality buildings that are landlord controlled.
"The market is currently starved of buildings along the M42 corridor that offer larger floorplates, so we will be looking to remodel the existing planning consent in order to ensure we are delivering a desirable, cost-effective solution for commercial occupiers.
"Whether we develop speculatively or wait for a pre-let will be dictated by the market."
Martin Hill, development director for BAM Properties, added: "It speaks volumes about the strength of the M42 market that IM Properties has chosen to take the whole of Fore Business Park.
"They inherit some remaining letting potential in Phase 1 and a superb consented site.
"It's both an excellent investment for them and it's proven to bear out the speculative development approach BAM adopts."
Savills acted for IM Properties while BAM was represented by CBRE.
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