The departure comes after a highly publicised row at the beginning of last year which saw Rawsthorn falling out with the museum's founder Terence Conran over a flower-arranging exhibition.
In an official statement, director Rawsthorn, ( pictured with Conran) said: 'Having contributed to the exciting expansion plan, I look forward to seeing the Design Museum going from strength to strength in the future.'
The museum hopes a new director will spearhead a funding drive to find the cash for a new £50 million home for the institution, which it hopes to build over the next few years for occupation in 2012.
A spokesman said officials were in talks with an unnamed architect over the redevelopment and have 'a specific site in mind'. Museum board member Terence Conran's architecture office has denied any involvement with the project.
According to a statement released yesterday, the museum's trustees have decided to 'make the project as inclusive as possible' by 'encouraging an open conversation with all segments of the design community and public' over new facilities.