The national minimum wage is to increase by 12p an hour for adults to £6.31 from October.
The Government also announced that the rate for 18 to 20-year-olds will rise by 5p to £5.03, and by 4p to £3.72 for 16 and 17-year-olds.
Ministers said they had rejected a recommendation from the Low Pay Commission that the rate for apprentices should be frozen, announcing a 3p an increase to £2.68 an hour.
Business Secretary Vince Cable said: "The independent Low Pay Commission plays a crucial role in advising the Government when setting the national minimum wage every year. It balances wages of low paid workers against employment prospects if the rate was set too high.
"We are accepting its recommendations for the adult and youth rate increases, which I am confident strikes this balance. However, there is worrying evidence that a significant number of employers are not paying apprentices the relevant minimum wage rate.
"Apprenticeships are at the heart of our goal to support a stronger economy, and so it is important to continue to make them attractive to young people. Therefore, I am not taking forward the LPC's recommendation to freeze the apprenticeship rate due to non-compliance, but instead am raising it in line with the youth rates. We are working on a series of tough new measures to ensure we tackle non-compliance issues across the board."
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Tim Thomas, of the manufacturers' organisation the EEF, said: "This announcement strikes a delicate balance between the need for an element of pay progression and the limitations employers face in accommodating pay rises.
"The modest increase in the apprenticeship rate is unlikely to negatively affect apprenticeship recruitment and of much greater importance is the raising of apprenticeships standards, better information and advice to students and ensuring that apprenticeships are truly employer-led and employer-driven."
TUC general secretary Frances O'Grady said: "Boosting the incomes of the low paid goes straight into the economy and wage-led growth must be part of the recovery so we would have liked to have seen minimum wage rates go up further, even if the Government has rightly rejected calls for a freeze.
"But we are pleased that ministers have increased the apprenticeship rate. This sends a positive signal about the importance of apprentices."