Muhammad Azhar Shabbir, 18, and Ali Athar Shabbir, 16, from Dewsbury, West Yorkshire, were last seen close to St Annes Pier in Lytham St Annes on Saturday evening.
Their 15-year-old cousin, also from Dewsbury, managed to swim to the shore.
The youngster, who was not named, remains in hospital.
Police were alerted at 6.55pm after concerns for their safety.
On Sunday police confirmed that HM Coastguard and RNLI colleagues found two bodies just after 3.15pm, about a mile from the pier.
A police spokeswoman said: “Whilst they have yet to be formally identified they are believed to be Muhammad and Ali Shabbir.
“Their family have been notified and are continuing to be supported by a specially trained officer.
“Our thoughts and condolences remain with them at this incredibly distressing time.
“Thanks again to our colleagues at HM Coastguard, the RNLI and the National Police Air Service for helping the search to find Muhammad and Ali, as well as everyone who has sent kind words.”
Coastguard rescue teams from Lytham and Fleetwood and the coastguard search and rescue helicopter from Caernarfon had been part of the operation.
They were joined by RNLI lifeboats from Lytham St Annes and Blackpool, independent rescue service Southport Lifeboat, together with Lancashire Police and North West Ambulance Service.
A message from the Editor:
Leeds has a fantastic story to tell - and the Yorkshire Evening Post has been rooted firmly at the heart of telling the stories of our city since 1890. We believe in ourselves and hope you believe in us too. We need your support to help ensure we can continue to be at the heart of life in Leeds.
Subscribe to our website and enjoy unlimited access to local news and information online and on our app. With a digital subscription, you can read more than 5 articles, see fewer ads, enjoy faster load times, and get access to exclusive newsletters and content. Click here to subscribe. For more details on our newspaper subscription offers click here.