The Equality and Human Rights Commission (EHRC) said it had contacted Labour after receiving a "number of complaints" about allegations of anti-Semitism within the party, and had "carefully considered" their response before opening the probe.
The EHRC said the investigation would seek to determine whether "unlawful acts have been committed by the Party and/or its employees and/or its agents" and if the party has "responded to complaints of unlawful acts in a lawful, efficient and effective manner".
Deputy Labour leader Tom Watson said he had "privately and publicly" warned the party it faced a "vortex of shame" if it failed to deal with anti-Semitism.
"I feel utter shame that this investigation is necessary but I truly hope that it will provide the means to finally root out anti-Jewish racism from our party once and for all," he said.
Labour said it would "cooperate fully" with the EHRC, and rejects "any suggestion that the party does not handle anti-Semitism complaints fairly and robustly".
A party spokeswoman said: "Labour is fully committed to the support, defence and celebration of the Jewish community and is implacably opposed to anti-Semitism in any form.
"We reject any suggestion that the Party does not handle anti-Semitism complaints fairly and robustly, or that the Party has acted unlawfully, and we will continue to cooperate fully with the EHRC.
"We support the efforts of the EHRC to draw attention to the obligations all political parties have under the Equality Act. But its ability to do so has been undermined by a 70% budget cut since 2010.
"Labour is the party of equality and in government we will strengthen the powers and functions of the commission.
"There has been a deeply worrying rise in anti-Semitism in the UK and across Europe. We are taking action to root it out of our party by strengthening our rules and procedures.
"But the issue can only be properly dealt with by all political parties working together to protect the interests of the Jewish community and to combat racism in politics, the media and in society more broadly.
"That includes the need for the Conservatives and other parties taking action to deal with racism in their own ranks."
The EHRC is likely to request interviews with key figures in the party and will have the power to demand access to correspondence, emails and other information to determine how Labour dealt with allegations of anti-Semitic discrimination.
The body has no powers to fine or prosecute organisations following investigation, but can make recommendations or draw up a legally-enforceable action plan.
Separately, the Muslim Council of Britain has urged the EHRC to open an investigation into alleged Islamophobia within the Conservative Party.
Jewish MP Luciana Berger, who cited the handling of anti-Semitism when she quit the Labour Party to join Change UK earlier this year, said: "For anyone who might look to play this down, the threshold to initiate this process is extremely high.
"That the Labour Party has even met the evidenciary threshold is damning."
Labour former minister Dame Margaret Hodge said it was a "disgraceful day" for the Labour Party and accused Mr Corbyn of failing to take the issue seriously.
The Jewish MP tweeted: "One of the most depressing in my 56 years as a member. Corbyn has completely failed from day one to take this issue seriously.
"The consequence is a full statutory investigation, he should hang his head in shame."
The president of the Board of Deputies of British Jews, Marie van der Zyl, welcomed the EHRC's decision.
She said: "We note that the last party to face a racism probe from the EHRC was the British National Party, which is a truly shameful indictment.
"In the past four years we have seen a large number of cases of antisemitism throughout the party from bottom to top. Despite the Jewish community demonstrating in their thousands outside Parliament, this has still not been addressed seriously by the party leadership.
"We will await with interest the EHRC report into racism at the heart of the UK's official Opposition."