The property giant is planning a refurbishment of the six-storey building and in the longer-term is looking to redevelop the site.
Minerva House currently totals 103,686 sq ft and is located next to Southwark Cathedral near Borough market.
The two tenants are Winkworth Sherwood LLP and Ipsos Mori UK Ltd paying a total rent of £3.4 million per year.
Toby Courtauld, Chief Executive of Great Portland Estates said: “We are delighted to have acquired Minerva House, the first purchase following our £140 million equity placing announced less than one month ago.
“This property meets our objectives of an accretive initial yield with an attractive prospective total return due to its low rents and multiple refurbishment possibilities.
“Longer term, this river-fronting site provides us with significant development potential.”