The former MP and Scottish Liberal Party leader died after collapsing in a Paris street on 27 July, the eve of his 76th birthday.
John Prescott, the former deputy prime minister, was among the congregation in St Andrew's Cathedral in Inverness, along with Lib Dem MPs and MSPs.
The former Liberal leader Lord Steel of Aikwood delivered the main eulogy, while other tributes were made by David Johnston, the peer's son, and Archie Fraser, a lifelong friend from Skye.
Lord Steel said: "Russell would not have wanted this to be a sad or over-solemn occasion. Yet we are all left still with a sense of shock at his sudden departure."
He said Lord Russell-Johnston was passionate about the Highlands, Scotland and Europe.
Among the messages of condolence was one from Maryam Rajavi, president elect of the National Council of Resistance of Iran. She said: "He was a man of values, principles and ethics who made a great contribution to the advancement of civil liberties and human rights."
Born in Skye, David Russell Johnston was a Liberal MP from 1964-97. He became the leader of the Scottish Liberal Party in 1974 and was deputy leader of the Scottish Liberal Democrats from 1988-89. He had been suffering from bone marrow cancer but continued to work for the Council of Europe on human rights.