Figures from Police Scotland show that the overall level of crime has fallen by 10%
Despite this fall, there were rises in the number of sexual crimes and rapes reported.
Reports of violent crime and anti-social behaviour also fell over the past year.
Police Scotland said the rise in reported rapes and sexual crimes did not necessarily mean more of these types of crimes were being committed, but that people were becoming more confident at speaking out.
In the first full year of Scotland's single police force the number of alleged rapes being reported to the authorities increased by more than a fifth to almost 1,700 while the level of sexual crimes recorded rose by 11.8%.
A quarter of all sexual crime reported to police was historic and almost a quarter of rape victims were under 15 years of age at the time the crime was alleged to have happened.
Det Supt Louise Raphael, lead officer for the National Rape Task Force, said: "Our assessment is that people are becoming more confident in speaking out, often regarding incidents which happened some time prior to contact being made with the police or other organisations.
"Changes to the legal definition of rape, the way we work with partners and improvements in the way we now investigate these crimes has influenced the number and type of cases we are seeing."
The data also showed that police had become more efficient in investigating these crimes with more than 75% of these cases being detected by officers.
Scotland's Chief Constable Sir Stephen House said: "The data clearly shows rises in sexual crime including the number of rape cases reported to us and investigated.
"We said from the outset of the single service that such crimes were under-reported and that we wanted to instil confidence in those who suffer at the hands of sexual offenders or domestic abusers.
"Police Scotland will continue to work strongly with partners to provide a united approach to addressing the issue of rape and domestic abuse."
He added: "We must tackle the offenders to reduce the number of victims we see day in, day out coming to us to report some horrendous crimes.
"These are crimes which occur across Scotland, in every community, with victims and offenders from all backgrounds. "
The statistics also showed that while the number of domestic abuse incidents fell by 1.8% to 58,976, the proportion of these resulting in a crime report rose to 57.6%.
Violent crime, including assault, robbery and attempted murder decreased by a total of 10%, although the number of murders remained the same as the previous year at 56.
Domestic abuse also continued to make up almost a quarter of violent crime recorded with one in four common assaults related to domestic abuse.
The amount of anti-social behaviour, vandalism and disorder also fell over the past 12 months.
The figures also showed that there were fewer road collisions and fewer people injured on Scotland's road network.
However, there was an increase in the number of people killed in collisions, with 191 people killed, an increase of 24 from the previous year.
The report also showed that efforts to tackle to tackle organised crime in Scotland had resulted in 2,677 arrests linked to serious organised crime with the Proceeds of Crime Act recoveries totalling Â£82m in cash and restraints.
Sir Stephen House concluded: "The publication of our management information today provides a 12 month profile of crime, offences and incidents across the country.
"Regardless of where or when a crime has taken place Police Scotland is committed to keeping people safe and will continue with every effort to provide routes for victims to come forward and ensure there are no hiding places for offenders."
More people are coming forward to report allegations of rape and sexual crime to the police, according to new figures.