Maciej Ciania, 34, was found dead at his flat in Dickson Street, Leith, Edinburgh, on January 14.
He had been stabbed multiple times in a "violent and brutal" attack.
Pole Grzegorz Gamla, 26, was found guilty of the murder after a trial at the High Court in Edinburgh.
The victim's sister, Aleksandra Poprawska, welcomed the verdict, saying: "Nothing will bring Maciej back but we are relieved to know that the person who committed this terrible crime will probably never hurt anyone again and no other family will suffer like we do."
Mr Ciania had lived in Edinburgh for a decade and always regarded the city as his second home.
More than 60 officers from Lothian and Borders Police were involved in the inquiry to find the killer.
Officers worked in particular with Eastern European communities in the city as well as Polish authorities in the UK and in Poland.
Gamla was traced to Poland and brought back to Scotland to stand trial.