Ms Mann, vice-principal of Exeter college in Devon, takes over as head of North East Surrey college of technology (Nescot) in September.
She believes her mother was the first female Asian immigrant to be employed in post-war Britain.
The Black Leadership Initiative, set up four years ago to encourage the promotion of ethnic-minority managers, is claiming her appointment as its latest success.
The BLI has a target, set by the Learning and Skills Council, of having nine ethnic-minority principals in place by 2009. Ms Mann's appointment brings the total to seven.
It is celebrating this week after winning the education section of the 2005 British Diversity Awards in London, beating 15 other entrants.
Ms Mann said: "My parents were both teachers in India but, when we arrived here, in 1966, my mother took a job as a cashier in Sainsbury's and later became a postwoman, before she set up her own clothing business.
"She was my inspiration when I took my first job in a college at the age of 24. I decided then I would be the first Asian woman principal. It has taken me 19 years to achieve that ambition."
She will succeed troubleshooting Bill Grady at Nescot. He was appointed for six months to kick- start the college's recovery process after it was graded inadequate by inspectors in March.
Ms Mann said she was interviewed for two principal jobs on the same day but it was the Nescot post that appealed to her most.
"Nescot gave me a warm feeling and I felt drawn to that place," she said.
"I could feel the energy there with people wanting to change and make a difference.
"Bill has already done a lot of good work and I feel I can take that forward into a successful re-inspection. It is not just about improving areas graded unsatisfactory, but making all provision excellent."
Asked if she would keep the strict dress code the college has just put in place, banning staff from wearing jeans and combat trousers, she replied:
"I was asked if I supported the code in my interview and, of course, I said yes."
Ms Mann said she plans to draw on the support of two other ethnic-minority women principals in the South-east region: Stella Mbubaegbu, at Highbury college in Portsmouth, and June Jarrett at Cricklade college in Andover, Hampshire.
The other ethnic-minority principals are Wally Brown at Liverpool community college, Daniel Khan at Grimsby, Sujinder Sangha at Stockton Riverside in Stockton-on-Tees, and Satnam Gill at the Working Men's college in London.
Ms Mann praised the support she received from the BLI and the Network for Black Managers, which, she says, gave her the confidence to go for a college principalship.
Accepting the diversity award on the BLI's behalf on Friday, BLI director Rajinder Mann said: "Our work has had an impact on individual development and on organisational cultural change across the sector.
"BLI engages both black and white staff in the solutions for eradicating race discrimination and promotes the growth of BME staff into middle and senior management positions."