Three judges unanimously declared the restrictions, introduced by former lord chancellor and justice secretary Chris Grayling, legally flawed.
Campaign group Rights of Women (ROW) said the judgment would help ensure more victims will get access to justice in a range of family law cases, enabling them " to split safely from their violent partner".
Sarah Clarke, ROW's solicitor at the Public Law Project - which brought the challenge, said: "We are very happy that the Court of Appeal has allowed this appeal.
"Legal aid provides for representation in proceedings enabling domestic abuse survivors to escape from abusive relationships, protect their children, and manage their finances.
"This judgment will help ensure that they can achieve access to justice."
At the heart of the case are the rules on eligibility for legal aid introduced as part of the Legal Aid, Sentencing and Punishment of Offenders Act 2012 (Laspo) - and in particular regulation 33 of the Civil Legal Aid (Procedure) (Amendment) Regulations 2014.
The appeal court - Lord Justice Longmore, sitting with Lord Justice Kitchin and Lady Justice Macur - unanimously decided regulation 33 "frustrates the purpose of the 2012 Act of granting legal aid to victims of domestic violence".
Overturning a High Court ruling upholding the regulation, the judges declared it "invalid" in so far as it denied legal aid in cases of "financial abuse" and imposed a two-year time bar on evidence that could be used to show domestic violence had occurred.
During a hearing in January, Nathalie Lieven QC told the appeal judges on behalf of ROW that the flawed nature of the bar was revealed by the case of "wife M", who cannot be identified for legal reasons.
Her husband had started legal proceedings to gain contact with the couple's children more than two years after they had separated, said Ms Lieven.
By then a caution the husband had received for a domestic violence offence was more than 24 months old and, because of the time bar, could not be relied on as verification that she was a victim of abuse.
Ms Lieven said no other potential evidence was in date, and M was not granted legal aid until she obtained a GP's report after suffering a breakdown when she faced her ex-husband in court without legal representation.
Ms Lieven said large numbers of victims were being refused aid because of the time bar. They were being left with the choice of paying a solicitor privately - often resulting in them going into debt - representing themselves, or doing nothing and continuing to be at risk.
New data showed that 40% of victims still did not have the required forms of evidence to access legal aid.
Allowing the ROW appeal, Lord Justice Longmore said Ms Lieven had produced "a formidable catalogue of areas of domestic violence not by reached by a statute whose purpose is to reach just such cases".
A Ministry of Justice spokesman said the appeal court judgment would be "carefully considered".
He said: "We are pleased the court confirmed the lord chancellor did have the power to set domestic violence evidence requirements.
"We will now carefully consider the two findings made about the period of time for which evidence applies and concerns about victims of financial abuse.
"We are determined to ensure victims of domestic violence can get legal aid whenever they need it.
"We have made it easier for victims of domestic violence to obtain legal aid, by ensuring a broader range of evidence qualifies. This has contributed to a 19% rise in the number of grants awarded."
ROW's director, Emma Scott, said: "We are incredibly pleased to have got this judgment. It is everything we would have hoped.
"It is so important that women can have access to legal aid for proceedings that enable them to split safely from their violent partner."
Lord Bach, Labour's shadow minister for legal aid, said the appeal court judgment was "a great result."
He said: "The public would be horrified to know that thousands of sufferers of domestic abuse could have been denied access to justice and some will have been forced to stay with abusive partners because of the Government's actions.
"Tory Ministers must now urgently rectify the situation, bring forward their review of their disastrous reforms to legal aid and address the concerns facing thousands of the most vulnerable people in society."