Mr Watson and Mr Davis will challenge whether the law is compatible with human rights
The High Court is to hear a legal challenge to the government's emergency surveillance law brought by two MPs.
The Data Retention and Investigatory Powers Act was fast-tracked through Parliament in three days last July.
It allows Britain's intelligence agencies to gather people's phone and internet communications data.
But former Conservative minister David Davis and Labour's Tom Watson will argue that the legislation is incompatible with human rights.
Individuals or organisations have the power to seek a judicial review of any decision by a public body that they believe has been made unlawfully.
The Data Retention and Investigatory Powers Act was rushed through Parliament in July 2014, after a ruling by the European Union's Court of Justice rendered existing powers illegal.
While a bill's passage through the Commons usually takes a matter of weeks or months, there are well-established procedures for fast-tracking legislation when MPs believe it is necessary to do so.
The government said at the time that without the new law, the UK's ability to fight crime and protect the country against terrorism would be seriously impeded.
New measures are being drawn up by the government to "address gaps" in intelligence gathering
Ministers said the act would simply maintain existing powers, which required communications companies to retain data for 12 months for possible investigation.
They said it would not allow police or security agencies to access the content of calls or emails without a warrant.
The plans were supported by the three main parties, but opposed by civil liberties campaigners.
However, Mr Watson and Mr Davis say the legislation was rushed and lacked adequate safeguards, and needs to be re-thought.
They will argue that the legislation is incompatible with the right to a private and family life, and data protection, under both the Human Rights Act and the European Union Charter of Fundamental Rights.
Their legal challenge comes as Home Secretary Theresa May draws up proposals to give police and spies new powers to monitor internet and phone use.
Downing Street said the measures, announced in last month's Queen's Speech, would "address gaps" in intelligence gathering and access to communications data that are putting "lives at risk".
However, civil liberties campaigners claim they will pave the way for mass surveillance of UK citizens.
Mrs May's efforts to introduce a similar bill in 2012, dubbed the "snooper's charter" by critics, were blocked by their coalition partners, the Liberal Democrats.