The two trespassers, whose faces are clearly visible on their video footage, also captured themselves using the slides in the leisure pool at the sports centre in their illicit visit.
They can be seen riding a bike around the poolside, swimming in the main pool, which is used for competitions, and floating in rings.
One of the explorers is also filmed tampering with poolside controls in the sports centre.
The video begins with the men walking into Ponds Forge through the main reception area, which is staffed and where others are milling around.
It is believed that the men then hid in the sports centre while final checks were carried out before the venue closed.
Security alarms did not sound while the men were in the centre and no security guards were seen.
The trespassers were able to roam around the sports centre and swim freely without being challenged during their visit, which was carried out in the early hours.
The video footage of their escapade begins with one of the men, wearing shirts and goggles, riding a bike into the pool.
The men can be seen playing in the water jets in the leisure pool and throwing floats and arm bands into the water.
One of the men cut his leg in the sports centre visit, with the blood visible on his leg in the video as he was poolside.
South Yorkshire Police has been informed of the incident.
Mandy Parker, General Manager at Ponds Forge International Sports Centre, said: "We have become aware of the video that has been posted on YouTube and, as a result of the footage, are instigating a thorough review of our building procedures throughout the venue including those with our security partners.
"It is disappointing that this incident has occurred and we’re investigating the reasons behind why it took place.
"On a wider point the irresponsibility of those who took part in the video beggars belief. We have strict safety policies in place for our leisure and competition pools - the diving pool for instance is almost six metres deep and requires specially trained staff available during opening hours in case of emergencies.
"There can be no excuse for this kind of ‘prank’ at a public venue which is for the use of everyone. It could have gone critically wrong. We will assist the police with their enquiries in any way we can."