Torin and Jacques Lakeman, aged 19 and 20, both attended Castle Rushen High School, in the south of the island.
The pair were found in a room above The Grapes in Stoneclough, Bolton, at 14:00 GMT on Monday.
A school spokesman said staff and pupils were "deeply shocked and saddened" to hear of the deaths of two "lively and talented" ex-students.
Greater Manchester Police said: "There are no suspicious circumstances surrounding the deaths".
However Aberystwyth University, where Torin was in his second-year, has emailed its students to pass on a warning from Dyfed-Powys Police about a "new strain" of the drug MDMA - also known as ecstasy.
Jacques Lakeman, who was a Castle Rushen student between  2005 and 2010, was described by his teachers as "as an intelligent and talented student who had a wicked sense of humour and a talent for playing the guitar".
He had recently left the Isle of Man to live in the UK.
The younger of the two brothers, Torin, attended the school between 2006 and 2013.
He was described as a "lively and popular student" who was "an eminently talented public speaker and a Corporal in the Isle of Man Combined Cadet Force (CCF)".
Torin was studying Physics with Planetary and Space Physics at Aberystwyth.
Tributes have been paid to two Isle of Man brothers found dead in a pub in Greater Manchester.