The families of both John Suddards and Betty Yates welcomed the murder verdicts and the life sentences passed on Stephen Farrow.
Mrs Yates, who was a widow, left behind her two children, Hazel and David, and many other family members and friends.
Mr Yates said outside court: "We should all be relieved and thankful that Stephen Farrow is off the streets of Britain today.
"It is clear from his own words that had he not been caught he would have continued to kill others and leave more misery in his wake.
"We have seen at first hand the complexity of this murder inquiry and we want to thank the police and everybody involved for their tireless work, their attention to detail and their consideration throughout this process.
"In the most difficult of times you rely on your friends and family, and we thank all of you for your help and good wishes over the past months."
His sister, Hazel Costello, said: "For our mother there is now some public justice, but our personal loss remains and will continue.
"For us it is important that our mum does not become defined by the brutality of her death, but is celebrated for the 77 years of her life.
"She will be remembered by her family, friends, colleagues and pupils as a woman who was kind, determined and above all good fun.
"We are not in denial about the circumstances of her death but we can and do choose to concentrate on the joy she gave in life. To do otherwise would be a betrayal."
Mr Suddards's sister Hilary Bosworth said: "Today we have reached the end of the trial of Stephen Farrow. The verdict is - in my view - a just one, which reflects the gravity of the situation.
"My brother John was a good man, who dedicated his life to serving God and helping other people.
"He was a much loved uncle to my three children, and a dear friend to so many, and he is greatly missed.
"In the nine months since John died, we have experienced all the grief of losing a loved one, but we have also had to come to terms with the fact that John's life was taken, in a very violent and totally unprovoked attack, in his own home.
"Thankfully for all concerned, only six days after the offence, Stephen Farrow was arrested."
Mrs Bosworth, from Dorset, added: "Like many other tragic events, the shocking deaths of John and Betty Yates raise many questions.
"How might things have been different? What could have been done to avert these tragedies?
"Do we, as a country, do enough to ensure that psychopaths, with a known history of violence and criminal offences, are not left roaming around at large, ready to attack someone?
"Do we perhaps need to think again about how me might better monitor those people in our communities who present a real risk to society.
"These are not questions for us here today, but they do, in my view, merit some serious consideration."