Ministers are concerned that Britain could be economically disadvantaged because of its workforce's lack of maths skills.
The new programmes will bridge the gap between academic, vocational and work-based study for sixth-formers, students and adults.
The most demanding units will carry university-entrance points in order to encourage more sixthformers to broaden their studies to include mathematics.
The new qualifications - called Free Standing Maths Units - will cater for non-mathematicians in schools, colleges and the workplace.
They will provide intensive coverage of the mathematics needed by other subjects - calculus for scientists, for example, statistics for psychologists or three-dimensional problem-solving for art and design students.
The units will be at three levels: "fondation" (equivalent to GCSE grades D to G), "intermediate" (equivalent to GCSE A to C) and advanced (equivalent to one-sixth of an A-level for university entrance purposes). However, the advanced units cannot be put towards AS, A-level or GNVQ qualifications.
Students who fail to get a C grade at GCSE are currently likely to drop maths completely. The new qualification will give them an opportunity to acquire maths skills that are relevant to their chosen career.
Teacher-trainees, for example, must currently have a C or better at GCSE maths, but officials at the Qualifications and Curriculum Authority hope the "intermediate" units may be accepted as an alternative.
The programmes have been piloted for two years.
Jack Abramsky, the QCA's principal subject officer for mathematics, said:
"There is a huge market for these qualifications. The maths units were designed to fulfil the different mathematics needs of students at different stages of their learning."