Local real estate agents said the house at one time had been listed for $10 million, the Austin American-Statesman reported.
The home, which Armstrong purchased in 2004, was appraised on the 2012 county tax rolls at $3.9 million.
Armstrong plans to stay in Austin, a spokesman said.
Al Koehler, 49, founder of a company that buys oil and gas royalties and mineral rights, purchased the 7,850-square-foot home and 1.7 acres of property.
Armstrong spent two years renovating the Spanish-style property. His office had a fireplace and leather-covered floors and a master suite featured a stainless steel fireplace. In 2008, the home was featured in Architectural Digest magazine.