It can take up to 6 months, but often around three. Some have managed it in weeks. A lot will depend upon your own particular case and your own particular creditors.
My opinions are merely that .. opinions based on experience. Always seek professional advice.
IVA Completed 23rd July 2013 .... C.C. 10th January 2014
Unfortunately it tends to depend on which firm you are with. It should only take a couple of weeks but some firms drag it out for up to 6 months. Keep the pressure on them to close quickly and if it takes longer than 6 months without a reasonable excuse make a formal complaint.