Mr Burke, 19, from Ripon in North Yorkshire, was last seen leaving Zero Zero nightclub in Bath on Thursday.
His body was recovered from a stretch of the river off Old Orchard on Saturday.
A post-mortem examination has confirmed he died as a result of drowning. Police have said the death is not being treated as suspicious.
Campaigners are calling for greater safety after several deaths in the River Avon in recent years.
The body of a man found in the River Avon has been formally identified as missing student Henry Burke.