The act, due to be implemented early in 2019, criminalises for the first time in Scotland controlling and coercive behaviours which can be a factor of domestic abuse.
SafeLives, a national charity dedicated to ending domestic abuse, will begin training officers later this year.
The charity said more than 130,000 people in Scotland live with domestic abuse every year, with 68 per cent of victims who access specialist support disclosing controlling behaviour, and 56 per cent physical abuse.
Assistant Chief Constable Gillian MacDonald, of the Crime and Protection Department at Police Scotland, said: “While physical assaults are the most visible part of domestic abuse, survivors have told us that it can be more difficult to cope with the punishing psychological abuse.
“This new act recognises, for the first time, the harm psychological abuse causes to victims and their children and the complex way in which perpetrators seek to manipulate not only their victims but also the police response.
“Ensuring our officers and staff are equipped with a good understanding of controlling behaviours is key to delivering this ground-breaking legislation.
“This training and the provisions within the new legislation will enable our officers to investigate and report not only the incident but also the wider circumstances of the abusive relationship.”
She urged anyone affected by domestic abuse to report it to the police or seek support from partner agencies.
The new domestic abuse law, which was passed by MSPs in February, covers psychological and emotional maltreatment, and coercive and controlling behaviour, as well as physical attacks.
Examples of coercive and controlling behaviour include isolating a partner from their friends and relatives or controlling their finances.
Suzanne Jacobs, SafeLives chief executive, said: “We are really delighted by today’s news. We now have the chance to change culture in relation to domestic abuse across the whole of Police Scotland.
“That’s a once in a lifetime opportunity to make life better for victims, survivors and their children all across the country. We look forward to delivering this work in collaboration with many expert partners from across the domestic abuse sector in Scotland, reflecting the diverse experiences of survivors and families.
“We know that together we can improve the response and ensure more people receive the right support, at the right time to keep them safe.”
The Scottish Government has provided £825,000 worth of funding to support the training.
Justice Secretary Michael Matheson said: “We’re doing everything we can to tackle the scourge that is domestic abuse at every opportunity and this new funding will greatly assist in tackling it.”