Wright qualified as an accountant at PwC and worked for the accountancy firm for nearly 15 years. She left in 2011 to join Save as director of financial governance, before joining Charity Projects, the charity that operates as Comic Relief and sister brand Sport Relief, last month.
A spokeswoman for Comic Relief said Wright had taken over responsibility for finance and facilities from Colin Simon, who retired as business director at the end of September.
Wright reports to Derek Gannon, chief operating officer of the charity, a new role created at the end of 2013, the spokeswoman said.
Charity Projects had an income of £114.2m in the year to 31 July 2013, the period that included the most recent Red Nose Day, Comic Relief's flagship event, on 15 March 2013.
Later in 2013, Comic Relief was in the news after it emerged that it had invested money in arms, alcohol and tobacco companies. After a review, it announced in May this year that it would stop making such investments and pledged greater future transparency of its investing practices.
Wright said in a statement: "Comic Relief is one of the UK’s best-loved charities, raising millions of pounds each year to help people living incredibly tough lives in the UK and Africa. I’m looking forward to bringing my experience in the private and charity sector to this new role, helping the charity continue its great work."