The content will be added to Virgin's on demand service under a new deal with US broadcaster HBO.
Other HBO shows on their way in HD include When the Levees Broke, Spike Lee's film about Hurricane Katrina hitting New Orleans.
Virgin says it offers more than 4,300 hours of content on its on demand service including HD programming from the BBC, Channel 4 and others.
Malcolm Wall, Virgin's chief executive of content, announcing the HBO content, said: "The public's appetite for high definition programmes continues to grow, so we're delighted to offer our customers two of the US' most popular and highly acclaimed shows in HD.
"We're constantly adding new films, TV shows and music videos to our already huge on demand service, but the addition of Band of Brothers and The Sopranos is a real coup."
On Demand Group (ODG) will handle the content management and promotion packaging of the content for the on demand service on behalf of Virgin Media.
