Robinson is currently chief executive of Manchester inward investment agency Midas.
She said: "Having spent six years as a non exec on the board of Manchester Central I was delighted to be approached to take on such an exciting role. Lesley has handed me a fantastic team of people and a venue that is now the envy of the industry."
Tomlinson, who will remain on the Manchester Central board, added: "This has not been an easy decision for me as this has quite simply been the best job I have ever had. I am really proud of what we have achieved over the last six years; the transformation of the building, the development of the brand and the hard earned reputation as a market leader."
Tomlinson oversaw a £30m redevelopment at Manchester Central.
Meanwhile, the Chartered Institute of Housing has announced that its Annual Conference and Housing Exhibition will move to Manchester Central from June 2012, generating an estimated £2m in economic impact for Manchester each year.