Those who rape or "seriously harm" women will be prosecuted in this country if charges are not brought abroad under the "unprecedented" agreement.
The new procedures would also cover offences such as forced marriage, female genital mutilation, and forced abortions which may not be illegal abroad.
Last night, Mr Cameron also said that stalking would be made a criminal offence. "Stalking is an abhorrent crime," the Prime Minister said. "It makes life a living hell for victims. That is why we are explicitly criminalising stalking to make sure that justice is done."
Currently, only murder and paedophile offences committed abroad can be prosecuted in British courts. In a joint statement to mark International Women's Day, the Prime Minister and his deputy said they were acting to tackle the "utter scandal" of violence and domestic abuse suffered by millions of women.
"The agreement is not just a piece of paper," Mr Cameron and Mr Clegg said. "It's going to lift the standards of protection for women across Europe, give greater support for victims and, crucially, bring many more perpetrators to justice. By signing the convention we would ensure that British offenders who commit their crimes abroad would still face justice in our courts. We believe rapists and abusive men from the UK who seriously harm women should face the same fate wherever they commit the offence.
"Our message must be loud and clear: there must be nowhere to hide."
Mr Cameron and Mr Clegg said that Britain already had some of the toughest laws to tackle domestic violence, but more needed to be done.
It was not clear last night whether ministers have faced pressure to introduce the procedures to prosecute foreign cases in this country, or whether women had made complaints to British police about abuse abroad. There was also little information about how the new prosecutions would work in practice.
The announcement was made amid growing concern in Downing Street that Mr Cameron is not appealing to women voters. The Prime Minister has also recently indicated his backing for increased support for rape crisis centres.
The Prime Minister will host a reception in Downing Street today to mark International Women's Day. Mr Clegg will open the London Stock Exchange this morning accompanied by well-known female business figures.