Lewis, the managing director of ITV Wales, will take up his new post at the end of October.
The 52-year-old Welshman beat 115 candidates to the position and succeeds David Moffett, who stepped down nine months ago.
WRU chairman David Pickering said: "I was overwhelmed by the quality of the candidates who applied for the post at the outset.
"I'm thrilled to have such an experienced Welshman taking up the biggest post in Welsh sport and entertainment.
"Roger has proved himself to be a dynamic and astute leader in the world of media and entertainment.
"He will bring a huge range of relevant management and communication skills with him to the group."
Lewis joins ahead of WRU's annual general meeting on Sunday where a record turnover of Â£40million will be confirmed - a 27% increase on the previous year.
His appointment had the unanimous support of the seven-man panel set up to fill the post and was officially approved by the boards of both the WRU and Millennium Stadium.
Lewis said: "My total focus and commitment will be on ensuring the business generates the power to give Gareth Jenkins and the Welsh team everything they require to fulfil their potential.
"The management of the WRU will do whatever it takes to restore Wales to the forefront of world rugby both on and off the pitch.
"We are committed to regularly competing with and beating our Six Nations colleagues and to contest with the best in the world.
"We will do this by ensuring our strong and prudent financial management continues. In recent years the WRU has performed brilliantly to turn this business around.
"It is my job now to build on this base, seize the many business opportunities that are available to us and ensure the monies we generate go back into the game."