Daniel Young, 30, was attacked in Kendor Gardens near Morden Underground station shortly after 08:00 GMT on Tuesday.
A post-mortem examination found he died from a stab wound.
A 35-year-old man has been arrested on suspicion of murder and is currently in custody.
On the day of the attack a 26-year-old man was arrested on suspicion of murder and wasting police time. He has been bailed.
Mr Young, originally from Paignton in Devon, was attacked as he made his way to the London Campus of Coventry University for the second day of a new job.
He was attacked in a park used by commuters as a short cut to Morden Tube station and Morden Road tram stop.
It happened less than 40 minutes after a 23-year-old man was stabbed in the buttocks in nearby Lewis Road.
Scotland Yard said it was investigating whether the two attacks were linked and trying to establish the motive and whether the attacker was known to Mr Young.
Meanwhile, an online fundraising page apparently set up in memory of Mr Young has been removed after his family reportedly said they had no knowledge of it.
Police said they understood that the donations made through the Gofundme page would be refunded. The Met's Cyber Crime Unit is investigating.
On Facebook, Mr Young's brother Simon wrote: "My Brother. My friend. I'm still wrapping my head round this, still hoping/wishing it's a sick joke.
"I don't know what to feel, I'm frustrated, angry, upset, confused. Just so proud of everything you achieved in your life, places you travelled, friends you made...you are inspirational big Bro."
Det Supt Paul Monk said: "I understand the concerns of the public that the attack on Daniel Young was unprovoked and potentially committed by a stranger in a random attack.
"We too share those concerns and have allocated significant resources to find the person who did this."
A second man has been arrested in connection with the murder of a university lecturer killed near a London Tube station.