Police have cordoned off a 200-metre area around the station
Met Police Commissioner Sir Ian Blair said the shooting was "directly linked" to the ongoing London bombs inquiry.
Police have said it is not yet clear if he was one of four bombing suspects shown on newly released CCTV footage.
A second man arrested at a flat in the Stockwell area is being held under the Terrorism Act, Scotland Yard has said.
Scotland Yard said the man arrested had been taken to Paddington Green police station in central London for questioning.
He is being held on suspicion of the preparation, instigation and commission of acts of terrorism.
They pushed him to the floor, bundled on top of him and unloaded five shots into him
Witness Mark Whitby
'They unloaded five shots' Shooting watershed for UK
Residents of flats between Carroun Road and Dorset Road said armed police had raided a flat at about 1630 BST and led away a man, woman and child, who were dressed in plastic boiler suits.
One neighbour, 42-year-old Adil Abdulla, said: "We heard some shouting and there were police with guns saying 'get inside', they were saying 'get down, get down'.
"The man said 'I'm doing it' and the police said to him 'if you don't do it, you are going to get shot'."
Scotland Yard said the man shot dead at about 1000 BST on Friday in Stockwell had still to be formally identified.
BBC correspondent Tom Symonds, in Stockwell, said it appeared his body had been taken from the station on Friday evening in a coroner's van.
The man was under police observation because he had emerged from a house that was being watched following Thursday's attacks, a Scotland Yard spokesman said.
He was followed by surveillance officers to Stockwell station, where his clothing and behaviour added to their suspicions, he added.
Police warned the man, who ran on to the station platform. Witnesses said the officers opened fire as he jumped on to a train.
'Pushed to the floor'
Sir Ian told a press conference: "I need to make clear that any death is deeply regrettable but as I understand the situation the man was challenged and refused to obey police instructions."
The incident is being investigated and, like all fatal police shootings, will be scrutinised by the Independent Police Complaints Commission.
Stockwell passenger Mark Whitby told BBC News he had seen a man of Asian appearance shot five times by "plain-clothes police officers".
"One of them was carrying a black handgun - it looked like an automatic - they pushed him to the floor, bundled on top of him and unloaded five shots into him," he said.
Police have cordoned off a 200-metre area around Stockwell station, where forensic officers are working amid sheeting and scaffolding.
Passengers were evacuated from the station, which is on the Northern and Victoria lines. Services on those lines have resumed but Stockwell, Oval and Warren Street stations remain closed.
BBC Home affairs correspondent Margaret Gilmore said officers had challenged a known suspect they had been following.
"He ran, they followed him. They say they gave him a warning, they then shot him.
"They brought in the air ambulance. They did everything they can to revive him. He died at the scene."
Questions asked
The Muslim Council of Britain said Muslims were concerned about a possible "shoot to kill" policy.
Spokesman Inayat Bunglawala said: "There may well be reasons why the police felt it necessary to unload five shots into the man and shoot him dead, but they need to make those reasons clear."
Another passenger on the train, Anthony Larkin, told BBC News the man appeared to be wearing a "bomb belt with wires coming out".
The man burst in through the door to my right and grabbed hold of the pole and a person by the glass partition near the door
Passenger Dan Copeland
Stockwell left in shock
Londoner Dan Copeland was in the carriage in which the man was shot.
He told BBC News: "We were sitting for a few minutes on the platform, then we heard shouting from the concourse between the two platforms.
"Then the man burst in through the door to my right and grabbed hold of the pole and a person by the glass partition near the door, diagonally opposite me.
"An officer jumped on the door to my left and screamed, 'Everybody out!'
"People just froze in their seats cowering for a few seconds and then leapt up.
"As I turned out the door onto the platform, I heard four dull bangs.
"I ran past an armed officer who was standing on the platform and ran up the stairs."
The bus driver found a rucksack split open on the top deck
Enlarge Image
1: Witnesses report seeing up to 20 plain clothes police officers chase a man into Stockwell Tube station from the street 2: One person says the man vaulted the automatic ticket barriers as he made his way to the platforms 3: The most direct route is via this escalator or the staircase that sits alongside it 4: Police challenge the man but he apparently refuses to obey instructions and after running onto a northbound Northern line train, he is shot dead
Did you witness the shooting? Send us your eyewitness accounts using the form below.
Name:
Email address:
Town and Country:
Phone number (optional):
Comments:
The BBC may edit your comments and cannot guarantee that all emails will be published.
Die U-Bahn-Station Stockwell auf der „Northern line“, mit gekennzeichneten Explosionsorten vom 21. Juli
 Wie der Fernsehsender Sky TV unter Berufung auf Polizeikreise berichtet, haben Polizisten einen Verdächtigen verfolgt, der in eine U-Bahn im Süden der Stadt (U-Bahn-Station Stockwell) flüchtete. Eine Sprecherin der Londoner Polizei bestätigte Meldungen, er sei erschossen worden.

Angeblich handelte es sich um einen der mutmaßlichen Attentäter, die gestern wieder für Angst in der Metropole gesorgt hatten.

Die Polizei hat einen 200-Meter-Bereich um die U-Bahn-Station Stockwell abgesperrt. Die Bahnlinien Victoria und Northern Lines wurden nach Aufforderung durch die Polizei eingestellt. Krankenwagen seien unterwegs zu dem Schauplatz in Stockwell.

Der Augenzeuge Mark Witby sagte gegenüber BBC, er habe in der U-Bahn gesessen und seine Zeitung gelesen, als er ein lautes Geräusch gehört habe. „Runter, Runter!“ hätten Leute gerufen. „Ich sah einen Asiaten in den Zug rennen, der von drei zivilgekleideten Polizisten verfolgt wurde. Einer von ihnen hielt eine schwarze Handfeuerwaffe - es sah wie eine Automatik aus - sie schubsten ihn zu Boden, hielten ihn von oben fest und gaben fünf Schüsse auf ihn ab.“
Der Verdächtige sei dadurch aufgefallen, dass er mit einem Wintermantel bekleidet gewesen sei.

Der Moslemische Rat von Großbritannien zeigte sich besorgt über eine mögliche „Todesschuss-Politik“. Ihr Sprecher Inayat Bunglawala sagte: „Es mag Gründe geben, warum die Polizei es für notwendig hielt fünf Schüsse auf den Mann abzugeben und ihn zu erschießen, aber sie werden diese Gründe erklären müssen.“

Ein anderer U-Bahn-Passagier, Anthony Larkin, sagte gegenüber BBC: „Ich habe diese Polizisten gesehen und sie riefen 'Runter, runter!' und ich sah diesen Kerl, der mir so vorkam, als hätte er einen Sprengstoffgürtel getragen mit Drähten, die da herausragten.“