Amie Gray, 34, was killed and 38-year-old Leanne Miles was seriously injured in the attack on Durley Chine Beach on 24 May after they were "chosen at random".
Nasen Saadi, 20, from Croydon, was found guilty following a trial at Winchester Crown Court, and pleaded guilty to failing to give the police access to his mobile phone.
The prosecution said Saadi "seems to have wanted to know what it would be like to take life".
Benjamin May, senior crown prosecutor with CPS Wessex, described the murder as a "senseless attack" which had shocked the people of Bournemouth.
"Though both victims were chosen at random, Nasen Saadi's unfathomable desire to carry out a murder was backed up by extensive planning – which included going to great lengths to avoid getting caught," he said.
"Now he has been convicted and faces life behind bars, I hope he will be forgotten."
Reading a statement outside the court on the behalf of Ms Miles, who was married to Ms Gray, Det Insp Mark Jenkins of Dorset Police, said she would "never be forgotten".
"Amie's life has been brutally taken, but now she can rest in peace," he read.
On the night of the attack, the two women were sitting on the sand where they had lit a fire.
Jurors were shown CCTV footage of Saadi walking up and down the promenade before stepping on to the sand and attacking the pair and leaving them to bleed to death.
Ms Gray, a fitness instructor, was pronounced dead at the scene after paramedics arrived.
Ms Miles was taken to hospital with 20 knife wounds, mainly to her back.
Saadi, who had been studying criminology at the University of Greenwich, was arrested at his aunt's house in Purley on 28 May.
Police found a number of knives and self-defence spray in a bedroom at the property.
No weapon or clothing from the night of the killing was recovered during the investigation.
In the police interview Mr Saadi told detectives he had an interest in unsolved crimes, such as the Setagaya family murders in Japan.
Saadi refused to disclose his passwords, and pleaded guilty to failing to give the police access to his mobile phone.
On his laptop, investigators found internet searches for "deadliest knife", "Why is it harder for a criminal to be caught if he does it in another town" and "What hotels don't have CCTV in UK", the jury was told.
He had also looked up "Bournemouth CCTV" and "Bournemouth pier CCTV" just days before the murder took place.
The jury was shown CCTV footage which Ms Jones said captured Saadi travelling from Croydon to the Travelodge hotel in Bournemouth on 21 May.
He carried out recces of the area before moving to the Silver How Hotel on 23 May.
In footage shown in court, detectives asked Saadi what he had done after checking out of the Travelodge on 23 May.
Saadi said "I can't remember, maybe sleepwalking… I probably blacked out" and told detectives his next memory was being at home on 25 May.
He told investigators he was a victim of "mistaken identity" and said "that's not me" after being shown CCTV footage from the night of the attack.
Saadi chose not to give evidence from the witness box, and Mr Sherrard, defending, did not give any further evidence.
He will be sentenced at Winchester Crown Court on 28 March.