Lt Cdr Ian Molyneux, 36, was shot on board HMS Astute as it was docked in Southampton on a "goodwill" visit on Friday afternoon.
A second officer was shot and is in hospital. A Royal Navy serviceman has been arrested on suspicion of murder.
Lt Cdr Molyneux, of Wigan, Greater Manchester, was in charge of the vessel's missiles.
His widow, Gillian, said: "Ian was utterly devoted to his family.
"Everything he did was for us. He was very proud to be an officer in the Royal Navy Submarine Service.
"He will live on in our four beautiful children."
First Sea Lord Admiral Sir Mark Stanhope said: "This is a very sad day for the Royal Navy and in particular the submarine service.'Good bloke'
"My personal thoughts and sympathies and those of the whole Royal Navy are with the family of Lt Cdr Molyneux, and that of the injured submariner.
"This incident is indeed tragic and the Royal Navy, in co-operation with the Hampshire Constabulary, will investigate this incident fully."
Capt Phil Buckley, captain of the Faslane Flotilla, to which HMS Astute belongs, said Lt Cdr Molyneux's family had the flotilla's "deepest sympathy".Ch Supt David Thomas: "Officers have questioned 20 witnesses"
"Ian Molyneux was a thoroughly professional and competent submarine engineer and a great asset to HMS Astute and the Royal Navy's Submarine Service.
"His loss will also be felt by his shipmates and across the service. He was, simply, a good bloke."
The injured crewman, who has not been named by the Ministry of Defence (MoD), is conscious and in a stable condition in hospital.
Hampshire Police said the full circumstances leading to the events had not yet been established but they were not related to terrorism.
Officers have been granted more time by Southampton magistrates to question the arrested man.Gunman overpowered
More than 20 witnesses have so far been questioned.
Ch Supt David Thomas said HMS Astute remained a crime scene and was yet to be released back to the MoD.Eleven children were waiting to board the submarine when the shooting happened
Earlier, the leader of Southampton City Council, Royston Smith, described how he overpowered the firing gunman while on a guided tour of the vessel.
He was on board with the city council's chief executive and mayor as part of a civic party.
Mr Smith, who once served in the RAF, described at least six shots being fired.
He said: "At some point I decided that the best form of defence was to try to disarm him. I guess I'm lucky he did not hit me."
The Port of Southampton has been fully reopened following the incident.
HMS Astute has been berthed in Southampton since Wednesday for a five-day official visit.
The 97m (318ft)-long craft is the UK's newest nuclear-powered attack submarine and is based at the Faslane Naval Base on the River Clyde.
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