Under the reform, survivors will be able to report abuse for up to 15 years after turning 35. Up until now, the clock started running from their 18th birthday.
Campaigners have long argued that many victims take years to digest the abuse they have suffered and report it, meaning that in many cases the offenders cannot be prosecuted.
The legislation won 297 votes in favour in the 350-seat parliament, with only the 52 lawmakers of far-right party Vox voting against it.
It also expands the definition of violence to include any type of physical, emotional or psychological abuse, including corporal punishment or neglect.
The law also identifies new crimes committed online such as incitement to commit suicide, commit sexual crimes or encourage bulimia or other eating disorders.
It will also create special courts for cases involving violence against children and minimise the number of times that children under the age of 14 must testify, to avoid further trauma.