The decision, announced by the Learning and Skills Council, follows concerns that training providers would have to cut the number of apprentices as the drop-out rate fell.
Training companies are given fixed-price contracts to train a specified number of starting apprentices. But these are based on assumptions that more than two-thirds will drop out before the end of their course, putting a cap on training costs.
As more students completed apprenticeships, the costs have risen, leaving training providers with a pound;25 million shortfall last year - the subject of a dispute with the LSC. The council said that the pound;41m would fund the rising success and ensure that the numbers of apprentices can continue to rise.
The Chancellor, Gordon Brown, has said he wants the number of apprentices to hit 320,000 within two years. At the moment, there are about 255,000.
Stephen Gardner, director of apprenticeships at the LSC, said: "The apprenticeship programme has experienced dramatic expansion and an improvement in quality over the last three years. Training providers have seen their incomes rise as more apprentices achieve results and they receive the associated achievement payment.
"We now need to use the additional funding to make more places available to match the demand from employers and young people, while continuing to increase quality."
A spokesman for the Association of Learning Providers, which represents many of the training firms providing apprenticeships, said: "If it's an effort to encourage the upward curve of completion rates to continue, then it's very welcome.
"The LSC is acknowledging there is an issue here. The Department for Education and Skills had already picked up on this. We were pushing at an open door."The funding of apprenticeships is also being reformed to reflect the costs of training for different jobs, with changes phased in over two years. It means that apprenticeships in children's care, learning and development, for example, will now receive more funding, while advanced apprenticeships in construction are among those judged to require less cash.
Kevin Street, senior policy manager for the LSC, said: "All the adjustments have been made after interviews with providers with long experience of delivering high-quality apprenticeships and with high completion rates.
"We needed to be sure that the best providers would be able to deliver for the funding that we have agreed."