The national minimum wage is to rise by 12p an hour to £6.31 for adults and by 5p to £5.03 for 18-20-year-olds from October.
Business secretary Vince Cable said the government accepted the recommendation of the Low Pay Commission.
However, although the Commission said the rate for apprentices should be frozen, Cable said it would rise by 3p to £2.68 an hour.
The increases are below current inflation levels.
Cable added that there was worrying evidence that not all employers are paying apprentices the minimum wage.
The following rates will come into effect on October 1, 2013:
* The adult rate will increase by 12p to £6.31 an hour
* The rate for 18-20 year olds will increase by 5p to £5.03 an hour
* The rate for 16-17 year olds will increase by 4p to £3.72 an hour
* The apprentice rate will increase by 3p to £2.68 an hour.
* The accommodation offset increases from the current £4.82 to £4.91