Ms Joseph started the £160,000-a-year role in May 2012 with a brief to attract new jobs, investment and visitors to the city.
The organisation said at its stakeholder meeting earlier this week that it had overdelivered on its job creation target in its second year of operation.
Mr Clarke, who is chief executive of Leeds-based supermarket giant Asda, praised Ms Joseph for “an outstanding contribution”.
He said in a statement: “Leeds and Partners has undergone a significant period of transition and transformation to reach its current phase of focusing on development and delivery.
“Under the leadership of its CEO, Lurene Joseph, the organisation has transformed the way that the city and wider region approaches inward investment and driving growth in the visitor economy. “As was recently announced at our annual stakeholder meeting, Lurene’s stewardship has delivered, among other things; the creation of over 1,200 jobs, £10m incremental spend in the visitor economy and the development of a mature investment pipeline; all of which is well over the target set and ahead of the timescale for delivery.
“As a result of the strategic investment approach put in place by Lurene and endorsed by UK Trade & Investment, the commercial collaborations formed with the private sector, nationally and internationally; combined with her focus on building a high performing organisation centred on outcomes; Leeds and the wider region has a solid foundation on which to build future growth. “
“Lurene believes that against this backdrop, the time is right for her to pursue new challenges in the private sector and to continue her work on private sector boards.
“She will be leaving Leeds and Partners in Spring 2015 having assisted with succession and transition planning.
“I would like to thank Lurene personally for her achievements during her tenure. She will leave a lasting legacy for future delivery.
“On behalf of the board of Leeds and Partners, I would like to express our appreciation for her outstanding contribution and support and to wish her well for the future.”
Her tenure was not without controversy. Last year, the organisation faced criticism over its spending on foreign travel.
Leeds and Partners defended the expenditure as necessary to meet with potential foreign investors.
Ms Joseph also faced a series of grievances from council staff involving alleged bullying but these were not upheld by an independent investigation, which reported its findings in December.
Leeds and Partners is funded by the taxpayer via Leeds City Council. It was formerly known as Marketing Leeds.