The pair were attacked after being called to reports of a man with a blade near Leicester Square at around 6am.
One of the Met officers has suffered multiple serious injuries.
The other was stabbed in the arm after they stopped the suspect near the junction of Shaftesbury avenue and Great Windmill Street.
Both officers are male and were in uniform.
A man believed to be in his 20s was arrested at the scene.
A police spokesperson said: “On Friday, 16 September at around 6am police encountered a male with a knife in the area of Leicester Square.
“Two officers received stab wounds and are currently being treated in hospital. We await further updates on their conditions.
“Taser was deployed and male was arrested on suspicion of grievous bodily harm and assaulting an emergency worker. He was taken to a hospital for treatment where he remains at this time.
“Enquiries into the circumstances surrounding the incident are ongoing.”
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