Ms Bryan, who joins Design Initiative from Arts Council England, says the design sector needs to find new sources of income if it is to continue its growth.
Design Initiative was founded in Liverpool in 1992 and opened a Manchester office in 2000.
It promotes the value of good design to businesses in the region and supports the work of designers through training, trade missions, exhibitions and events such as the Liverpool Design Festival, which will be held in November.
Ms Bryan has 16 years' experience in the arts world. She spent the early part of her career working in galleries including Manchester Art Gallery, the Henry Moore Institute in Leeds and the Cornerhouse Gallery in Manchester. She joined the Arts Council in 1999 and has held a variety of regional and national roles promoting design and organising the distribution of Lottery and Treasury funding.
Ms Bryan said: "I have long admired the work of Design Initiative, which is one of only a small handful of organisations of its type in the country.
"During its 18-year history, it has made a significant contribution to the success of the design sector at both a regional and a national level.
"My aim is to build on this track record, while at the same time finding new ways to contribute to the sector's success, for example through new services, new partnerships and new sources of income."
Design Initiative chairman Geoff Allman said: "Tanya is well-known and respected within the art and design sector.
"She is ideally placed to take the Design Initiative forward and further develop its role as a champion for the design sector."