South Korea's Constitutional Court has formally removed President Park Geun-hye from office over a corruption scandal, sparking rallies that have left two people dead.

The country's first female leader has been accused of allowing a close friend to profit from her connections with the presidency, and was impeached in December after weeks of protests aimed at securing her resignation.

Ms Park's "acts of violating the constitution and law are a betrayal of the public trust" Constitutional Court acting chief justice Lee Jung-mi said.

"The benefits of protecting the constitution that can be earned by dismissing the defendant are overwhelmingly big.

"Hereupon, in an unanimous decision by the court panel, we issue a verdict: We dismiss the defendant, President Park Geun-hye."

Her lawyer, Seo Seok-gu, who had previously compared Park's impeachment to the crucifixion of Jesus, condemned the verdict as a "tragic decision" made under popular pressure.

Thousands of people celebrated the historic decision on the streets of the capital Seoul, with polls showing that between 70 and 80% of South Koreans had wanted the court to throw Ms Park out of office.

The rallies took a tragic turn, however, when a 72-year-old man and supporter of Ms Park was injured. He later died in hospital, according to Yonhap News Agency.

A South Korean hospital said he had suffered head injuries after falling from a police bus.

South Korean police said that a second person had also died while protesting against Ms Park's removal.

First democratic leader to be removed from office

Ms Park had maintained her innocence throughout the impeachment proceedings.

But the ruling means she is the first leader to be removed from office since the country became a democracy in the late 1980s.

It also opens her up to criminal proceedings.

Under South Korean law a sitting president is immune from prosecution for most alleged crimes, but now that she is no longer in power prosecutors can summon, question and even arrest Ms Park.

An election is expected to be held within two months to choose her successor.

A likely candidate is liberal Moon Jae-in, who lost to Ms Park in 2012 but now leads the polls.

Whoever wins the election faces a faltering economy and the challenge of dealing with hostile neighbour North Korea.

There are also fears Ms Park's sacking could spark violence between her supporters and opponents.

One of her lawyers last month warned there would be "a rebellion and blood will drench the asphalt" if she was ousted.