It is possible to be a great nation without pretending to be a great power, he said in the inaugural Caledonian lecture at Glasgow Caledonian University's New York campus.
Mr Salmond is in the US as part of Scotland Week, an annual celebration of cultural links with North America.
He focused his speech on Scotland's contribution to the world and the well-being of all, linking it to the university motto: for the common weal.
Looking to the future, and possible independence, he said Scotland will be a good global citizen.
"You can aspire to be a great nation, without desiring to be a great power. The USA is both but most nations can't be, and they reduce their chance to be a great nation if they pretend to be a great power," he said.
"For most countries, greatness can only come from influence, not force; from soft, not hard power; from enlightened self-interest, not self-interest alone.
"It will come from their people, their values, their reputation and their ideas and it starts with good governance at home."
He described his ambition to promote Scotland's influence in "climate justice", international development and conflict resolution, as well as the generation of sustainable electricity.
While noting Scotland's military tradition, he told the audience he is proud to represent a country where the most celebrated figure is the poet Robert Burns.
He also touched on the potential for small nations to make a name for themselves in the world.
"Norway has gained global recognition for its peace-making efforts in conflicts and disputes, for example in the Philippines, Sri Lanka, Sudan, Colombia and the Middle East," he said.
"You could also look at Ireland's role in peacekeeping; Switzerland's contribution to humanitarian efforts; Finland's reputation for research and development; or the way in which Singapore is widely studied for its approach to economic development.
"The overall point is clear. Countries can exercise influence through the scale of their ambition and the strength of their ideas, rather than the size of their armies, their populations, or their territories.
"That will be true of Scotland, too. If you think for a moment about Scotland's past, the reason I'm here in the USA at this particular time is because of ideals of liberty and elective governance which were distilled in the Declaration of Arbroath almost 700 years ago.
"And in Central Park, where the Scotland Week run took place on Saturday, there are two statues of Scots, they're both of writers - Robert Burns and Sir Walter Scott.
Describing Scotland's place in the world, he said it will be an enthusiastic member of the EU, part of the British-Irish Council, and a "constructive" partner in Nato.
"We won't have nuclear weapons - nobody seriously believes that a nation of five million people should be a nuclear-armed power. But we will co-operate fully and constructively with our neighbours and partners, like the 25 Nato members - out of 28 - which are not nuclear powers.
"And we will join 193 other members of the United Nations, demonstrating a strong commitment to international law, and working with partners from around the world."