The 29-year-old disappeared on February 10 after attending his brother’s Eamonn’s celebrations in the city.
An extensive search was launched to find him and a social media campaign was launched after he disappeared.
Members of his family travelled to Hamburg after CCTV footage of the musician was discovered.
His body was discovered by German police the River Elbe on April 23 after a 10-week search.
Mr Colgan’s funeral was held in Inverness.
His family thanked people in Scotland and Germany for their “incredible support” during the search and paid tribute to Mr Colgan.
A statement on the Facebook page set up for the search said: “Whilst we still await confirmation regarding the circumstances surrounding Liam’s death there would be appear to be no suspicious circumstances and this has been a tragic accident.
“Liam was a much loved son, brother, brother in law, uncle, nephew, cousin and friend to so many.
“He was a hugely talented yet humble musician. He had a very natural sense of humour that made him a joy to be around. He cared for his nieces immensely and would visit them at every opportunity, they miss him greatly.
“Liam had a laid back, selfless personality that made him impossible not to get on with.”