Metropolitan Police Commissioner Sir Mark Rowley said that, in addition, a male officer was stabbed three times in the neck and once in the chest.
The injured officers were taken to hospital for treatment after the incident took place at around 6am; their injuries are not life threatening.
Scotland Yard confirmed that officers used Taser stun guns and a man, believed to be in his 20s, was arrested at the scene.
He was arrested on suspicion of causing grievous bodily harm and assaulting emergency workers.
The suspect has been taken to hospital as police investigate the circumstances surrounding the incident. It is not thought to be terror-related.
The officers – both attached to the Met’s Central West Command Unit – were carrying out routine duties and were not part of the wider policing operation in place following the death of Queen Elizabeth II.
The incident took place in London's Leicester Square
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Superintendent Justin Browne from the Central West Command Unit, responsible for policing Westminster, said:“Every day, police officers got out on the streets to keep the communities of London safe.
"In doing so they often have to put themselves in the way of danger, putting their own welfare at risk in order to protect others.
“The actions of these two officers, and their colleagues, exemplifies the key value of courage that runs through the core of the Metropolitan Police and they will be offered all the support they need as they begin their recovery from this terrifying incident.”
London Mayor Sadiq Khan condemned the attack, and called for anyone with information about the incident to contact police.
He said: “This attack on serving police officers in Soho overnight is utterly appalling.
“These brave officers were doing their duty and assisting the public at this momentous time for our country.
“My thoughts and prayers are with them, their loved ones and police colleagues following this disgraceful attack.
“Our police officers run towards danger to protect others and keep us safe and we owe them a huge debt of gratitude.
“I have spoken with the new Commissioner Sir Mark Rowley about this awful incident and remain in close contact.
“Attacks against the police will not be tolerated and any perpetrators will be caught and prosecuted.
“I urge anyone with information to come forward to ensure the perpetrator of this disgusting attack feels the full force of the law.”
