Eight other people were recovered from the water after getting into difficulty off the main pier as thousands of beachgoers enjoyed the sunny half-term weather.
They were treated by paramedics for non-life-threatening injuries.
An investigation into the circumstances surrounding the incident has been launched by Dorset Police, the Marine Accident Investigation Branch and the Maritime and Coastguard Agency.
Dorset Police said the two deceased - a 17-year-old boy from Southampton and a 12-year-old girl from Buckinghamshire - sustained “critical injuries”.
Police said that, following initial enquiries, a 40-year-old man - who had been on the water at the time - has been arrested on suspicion of manslaughter. It is believed the man was on a jet ski.
What we know about the area
Jet skis and other watercraft operating in the Bournemouth and Poole areas must follow specific rules between April and October.
Bournemouth, a popular seaside town on England’s south coast, is popular with locals and tourists during the summer months.
Average temperatures in and around the pier area of the sea are 12.4C for the month of June and can exceed 16 in September, according to the surf-forecast website.
The website says the area tends to receive a mix of “groundswells” and “windswells”, with surfers warned to “watch out for rips and crowds.
Bournemouth Pier, like all outcrops in the ocean such as groins, headlands or sandbars, presents danger for swimmers due to riptides, or rip currents.
Rips, as they are commonly known, occur when water that has been pushed towards land by the sea, is tracking back out, creating a channel of water which pulls back out to sea.
Rips are often harmless, and swimmers will barely notice them, but typically around large headlands or piers, they can be powerful and drag unwitting swimmers and surfers out to sea, particularly if there is a large swell running.
Piers and cliffs also present a hazard in summer because of the popular pursuit of ‘tombstoning’, or cliff-jumping, where thrill-seekers throw themselves into the sea off of the side of these outcrops.
Frequently people unfamiliar with conditions are hurt, or even killed, due to shallow water, hitting people in the ocean below, or landing in a dangerous position.
The sea conditions in Bournemouth when the incident happened appeared to be calm, with very little swell running. The water temperature was 15 degrees, meaning a wetsuit is required to swim comfortably.
The tides at Bournemouth see two highs and two lows in a 24-hour period. Like the rest of the UK, the tidal range is large, exposing large swathes of sand at low tide.
Low tide on 31 May was at 1:44pm and it was a 1m tide, while high tide was at 7:35pm and was 1.89m - making it a large tide.
This means the incident happened at mid-tide when the water would have been pushing shorewards.
What else have the police said?
At a press conference on Thursday, Dorset Police dismissed reports that the deceased had jumped from the pier or had been hit by a jet ski.
Rachel Farrell, assistant chief constable, confirmed that none of the swimmers had been in "physical contact" with any vessel.
She said that a number of people already in the water got into difficulty and the force was investigating what “caused that to happen”.
“As we have a person in custody, you will know there is only limited information I can give about the investigation,” Ms Farrell said.
"However, to avoid further speculation, I am able to tell you that it’s clear that yesterday a number of people already in the water got into difficulty and we are investigating the circumstances or event that caused that to happen.
Ms Farrell added that the two who died were not related to each other and those involved were "different people from different families" who were assisted by "great-spirited members of the public".
She added: "We are all truly devastated that two young people have lost their lives.
"My thoughts and those of all the emergency services are very much with their loved ones at this horrendous time and we are doing all we can to support their families."
Ms Farrell added: "As you can imagine, we are at the early stages of our investigation, and we would ask people not to speculate about the circumstances surrounding the incident to both protect our inquiries and out of respect for the victims and their families.
"We are aware of a number of videos circulating on social media and we would urge people to refrain from doing this.
"We know the beach was very busy when the incident occurred. I am today urging anyone who saw what happened or has any information that may assist to please come forward.
"If anyone has relevant phone footage then they can contact Dorset Police through our major incident public portal where they can upload the images and we will share the links on social media.
"This operation is named Operation Marble. So please share the images with the police rather than on social media."
She added: "I would sincerely like to thank members of the public who helped people in trouble in the water and also I am very grateful to wider beachgoers who really quickly moved from the beach to allow emergency workers do their work."
Witnesses see beachgoers filming aid effort
People on the beach said they witnesses other beachgoers filming paramedics delivering CPR to people involved in the incident.
Nicola Holton, who was at the beach with her husband, said she witnessed lifeguards entering the sea trying to help “multiple people” who were struggling in the water.
“[There were] loads of idiots ignoring lifeguard requests to get out of the water and clear the beach,” she said.
“People were running towards those having CPR filming on their phones.”
A doctor who said he was involved in the resuscitation attempt on the young girl praised the work of the beach lifeguards and also hit out at those filming the incident.
“Those videoing the desperate CPR attempts should think long and hard at their actions, the tragic death of a child is not something anyone should voyeuristically observe”, he told MailOnline.
Council to assess safety of sea near pier
Bournemouth, Christchurch and Poole Council leader Vikki Slade said the authority is working with the emergency services and will be assessing safety in the water near the pier.
“There are specific rules relating to the buoys in the water but there is no evidence that any of these rules have been breached,” she said.
Tobias Ellwood, the MP for East Bournemouth and chair of the Commons defence committee, told Sky News that the pier was “involved” in the tragedy.
The local council will review its protocols in relation to what can be conducted on the pier, he added.
Bournemouth West MP Conor Burns said the incident is a “salutary lesson” that “danger is ever present” on beaches and the ocean.
Beachgoers shocked at tragedy
Families arriving at the beach on Thursday spoke of their shock at the previous day’s events.
One woman, who did not want to be named, said: "It’s such a shame, people just come here to have fun, it’s a real tragedy."
Mourners were seen placing a bunch of flowers on the beach close to the pier early on Thursday morning.