Janet and John Stocker, aged 63 and 74, were killed in Sousse on Friday their family confirmed.
The couple, who had five children and 10 grandchildren, "tragically lost their lives as a result of Friday's atrocities" a statement said.
A minute's silence will be held on Friday to remember all the victims.
The family statement said: "Mum and dad were the happiest, most loving couple who enjoyed life's simple pleasures as well as the pleasures and love of their extensive family and their many friends.
"But most of all they were still very much in love with each other."
It said they were "both young at heart" and enjoyed "travelling to new places, exploring and appreciating local cultures, and they died together doing what they enjoyed most; sunbathing side by side".
Mr Stocker was a retired printer "born and bred in Peckham" while his wife came from Fulham and was a "fun-loving and devoted mother".
The family said: "They made a huge impact on our lives, and touched the hearts of so many people and they will both be sorely missed and never forgotten."
Britons killed by the gunman have started being repatriated to RAF Brize Norton ahead of a joint inquest being opened by the West London coroner.
One Belgian and one German are also thought to be among the dead.
Tunisian authorities have arrested several people on suspicion of helping the gunman Seifeddine Rezgui, who had links to the jihadist group Islamic State (IS). Rezgui was shot dead by police.
A couple who were "born and bred" Londoners have been named among the 38 people killed in the Tunisian beach attack.