The children's charity Barnardo's has said the move - which was voted by 101-0 at Holyrood yesterday - will send a clear message that it is "not acceptable" - with jail terms of up to seven years.
Only four MSPs abstained in the vote after Holyrood's Justice Committee had called for the Scottish Government to consider if it would be practical for to introduce its own legislation on the issue.
In a written submission to the committee, Mark Ballard, head of policy at Barnardo's Scotland, said: "We believe that creating an offence under Scots law of forcing someone into marriage would be the right step to take in order to tackle this very serious issue.
"We believe that, much like the attitude towards domestic abuse, cultural and societal attitudes towards forced marriage need to change. Making it a criminal offence to force an individual into marriage will send a clear message this behaviour is not acceptable."
He said that, currently, victims may be unwilling to come forward as they "may even feel as though they do not want the perpretrator punished by a criminal sanction".
He added: "By criminalising the act itself we will begin to shift perceptions and start the drive towards cultural change that is needed to stamp out forced marriage in Scotland."
Alison Davies, manager of Saheliya, an Edinburgh-based organisation which provides mental health support for black and ethnic minority women, said: "We believe it will strengthen support work and preventative work.
"Forced marriage should be in line with other abusive practices within the family such as domestic violence and sexual abuse."
Currently there is no criminal offence of forced marriage in Scotland but courts can issue protection orders to those at risk, which if breached could carry a two-year prison sentence.
Without forced marriage being a criminal offence the country risked failing to comply with the Council of Europe's convention on preventing and combating violence against women and domestic violence, also known as the Istanbul Convention.
The legislation will make it a criminal offence for someone to use violence, threats or any other form of coercion to force another person into a marriage - with this offence having a maximum custodial sentence of seven years.
Minister Shona Robison said that forcing someone to get married against their wishes was an abuse of their human rights.
She said: "Forced marriage is thankfully not an issue that affects the majority of people in Scotland. However, it is a blight on those communities where it happens and can have a devastating effect on the lives of victims."
She told how seven forced marriage protection orders had been granted since Scottish legislation was passed in 2011.
Ms Robison added: "We're seeking to go further in the protections available for victims by creating a new criminal offence of forced marriage through the legislative consent motion on the Antisocial Behaviour, Crime and Policing Bill going through Westminster."