Wright was the daughter of a well-to-do Scottish merchant and political radical who had circulated the works of Thomas Paine (Paine, Thomas). Her parents died and left her and a sister a fortune when she was two, and they were reared in London and Devon by conservative relatives. At age 21 she returned to Scotland to live with a great-uncle, who was a professor of philosophy at Glasgow College. There she read widely and wrote some youthful romantic verse and A Few Days in Athens (1822), a novelistic sketch of a disciple of Epicurus that outlined the materialistic philosophy to which she adhered throughout her life. In August 1818 she sailed with her sister for America for a two-year visit, during which her play Altorf, on the subject of Swiss independence, was produced in New York City.

The enthusiasm of her highly laudatory and widely read Views of Society and Manners in America, published in England in 1821, won Wright the friendship of the marquis de Lafayette (Lafayette, Marie-Joseph-Paul-Yves-Roch-Gilbert du Motier, marquis de), whom she visited in France in 1821. She timed her return to New York on a second trip in 1824 to coincide with his triumphal tour of the country and followed him on his entire journey. She joined him in visits with Thomas Jefferson (Jefferson, Thomas) and James Madison (Madison, James). Slavery was discussed, and both men approved in general of her plan to purchase, educate, and emancipate slaves and to help them start a colony outside the United States.

In 1825 Wright published A Plan for the Gradual Abolition of Slavery in the United States Without Danger of Loss to the Citizens of the South, which urged Congress to set aside tracts of land for the purpose. In December 1825, by way of demonstrating her plan, she invested a large part of her fortune in a 640-acre (260-hectare) tract in western Tennessee (near present-day Memphis) that she called Nashoba. She purchased slaves in 1825, freed them, and settled them at Nashoba with the promise of eventual freedom. The colony got off to a poor start, from which it never recovered.

During Wright's absence in 1827 owing to ill health, a scandal broke over charges of free love; on her return to Nashoba in company with Frances Trollope in January 1828, she found a ruin. After publishing a widely reprinted newspaper article defending her idea, she left Nashoba for Robert Dale Owen (Owen, Robert Dale)'s socialist community at New Harmony, Indiana. In 1830 she returned to arrange for the emancipation of the Nashoba slaves and their colonization in Haiti.

Wright helped edit Owen's New Harmony Gazette and, defying convention, took to the lecture platform. Her Course of Popular Lectures (1829 and 1836) attacked religion, church influence in politics, and authoritarian education and defended equal rights for women and the replacement of legal marriage by a union based on moral obligation. In 1829 she and Owen settled in New York City, where they published a radical newspaper called the Free Enquirer and led the free-thinking movement, calling for liberalized divorce laws, birth control, free secular education run by the state, and the political organization of the working classes. She lectured regularly in her “Hall of Science,” a converted church on Broome Street.

In 1830 Wright sailed to France with her failing sister, who died a short time later. In July 1831 she married Guillaume Sylvan Casimir Phiquepal D'Arusmont, a physician she had first met at New Harmony, and she remained with him in Paris until 1835. In that year they returned to the United States and settled in Cincinnati, Ohio. In 1836 and 1838 she was again on the platform, this time in support of the Democratic Party and in particular of President Andrew Jackson's attack on the Bank of the United States. Her own lecture courses attracted little attention, however. Over the next dozen years she traveled frequently between the United States and France. Wright and her husband were divorced in 1850.