Police Scotland has seen an 81% increase in reports of domestic rape and a 55% rise in reports of domestic stalking offences after its first year.
The organisation's festive campaign will target those suspected of domestic abuse.
Police Scotland recorded 58,976 domestic incidents in 2013-14.
Chief Constable Sir Stephen House gave the figures during a speech to a domestic violence conference in Edinburgh.
There were 1,690 reported rapes in 2013/14, up from 1,372 the previous year, while overall reported sexual assaults - including rape - rose 11% to 8,604 from 7,693.
The figures detailing domestic rape were not included in the statistics earlier this year.
However, Sir Stephen revealed there were 357 domestic rapes reported in 2013-14 compared to 197 in 2012-13. Domestic stalking cases increased from 367 in 2012-13 to 569 the following year.
Police said a large number of the sexual assaults can be attributed to an increase in reporting by victims and a rise in historical victims coming forward which may have been driven by the high-profile celebrity sex crime cases of the last year.
'We will find you'
The chief constable said that more than 20% of all police operational time was spent dealing with domestic incidents.
He said a domestic incident was reported somewhere in Scotland every nine minutes, on average.
He added: "The significant increase in the numbers of people coming forward to report these crimes is encouraging as it shows more and more are confident in the support they will receive but I believe these figures will be the tip of the iceberg.
"Over the Christmas period we will be running a festive campaign specifically targeted at those who commit these crimes. Many victims are especially vulnerable, often isolated and frequently in danger over the festive period. Abuse can escalate with victims suffering repeatedly at the hands of a partner or ex-partner.
"Our festive campaign will start the week before Christmas and we will have extra police officers on the streets across Scotland. It will have a direct focus on preventing abuse and sending a clear message that there is no hiding place - if you do it, we will find you."