Officers said forensic tests confirmed human remains recovered from the sea last month were those of 16-year-old Daniel McNeil.
Daniel, from Tynemouth in North Shields, went missing after his boat and the Scottish Viking passenger ferry collided in the North Sea.
The teenager was on board the Homeland vessel with his brother when it made contact with the ferry five miles off the coast of St Abbs in Eyemouth, Berwickshire, on 5 August.
His 20-year-old brother - who is the fishing boat's skipper - was pulled from the water by another vessel.
Police said inquiries are still under way to determine the circumstances surrounding the collision and they are liasing with other agencies.
Detective Inspector Jim Robertson, of Lothian and Borders Police, said: "Finally, Daniel McNeil's family has some closure following his identification and our deepest sympathies are with them at this time as they come to terms with their loss.
The passenger ferry was run by Norfolkline, part of DFDS Seaways, which operated services between Rosyth, Fife, and Zeebrugge in Belgium.