What was the first successful non violent independence movement?

Canada was not de jure sovereign- indeed, the process was still dragging on through the Ninety Seventies.

I'd say the first true example is Norwegian independence in 1905, because they chose a King from a different dynasty. Everything was on the basis of legal actions and the holding of plebiscites and thus Norwegian independence qualifies as achieved by non violence.

After that, Egypt was a British Protectorate for a few years. The British unilaterally declared it independent in 1922. However, they still had bases there so this was somewhat cosmetic. The same is true of Iraq which was a British mandate and became formally independent in 1932. The Second World War killed off Imperialism. It is arguable that all countries which became independent subsequently only did so because of cataclysmic changes brought about by that War. On the other hand, the US may have granted independence to the Phillipines (which became independent in 1946) anyway. Similarly, had a Labor Government had a stable majority in the U.K then India and Ceylon and so forth may have gained formal independence in the early Thirties.

The reason the Second World War changed everything was because Colonies realized that they would have to defend themselves. They could not rely on the Colonial power which might itself be under attack. The reverse point could also be made. The investors in the Colonial power realized that their own Navy and Army would not be able to defend their investments in distant Colonies. Why? Their own working class would not be prepared to go fight and die in distant corners of the globe to maintain the wealth of the upper class. Thus colonized countries needed to become independent and able to defend themselves. There were some exceptions- e.g. Cyprus which was strategically important, or Kenya, which had some White settlers- to the rule that after the Second World War, the Brits tended to prefer peaceful handover of power and sovereignty. The French, sadly, initially took a less sensible course.

How about Canada? Now, it wasn't exactly an independence movement, but here goes.

After the American War of Independence Britain's empire was diminished substantially, leaving Canada as England's chief North American possession. Yet, there were still many French settlers in Canada, and they did not get along very well with the British. In 1791, British prime minister William Pitt the Younger divided Canada into two sections (the British section and the French section) to ease tensions. But by the 1830s, Canada was again in turmoil.

Queen Victoria sent Lord Durham to investigate conditions in The Canadas, and he made these suggestions:

1. Reunite the two sections of Canada into one country.
2. Give the Canadians a representative government.
3. Follow a plan for settlement of unoccupied territories.

His plan was gradually enacted, and in 1867, the British North America Act made Canada a self-governing commonwealth.

Probably the more appropriate answer is strike actions in general, as also Gandhi did a long hunger strikes himself. Labour strikes date back at least to the strikes of Deir el-Medina:

In about the 25th year the reign of Ramses III (c. 1170 BCE) the laborers were so exasperated by delays in supplies they threw down their tools and walked off the job in what may have been the first sit-down strike in recorded history. They wrote a letter to the Vizier complaining about lack of wheat rations. Village leaders attempted to reason with them but they refused to return to work until their grievances were addressed. They responded to the elders with "great oaths". "We are hungry", the crews claimed; "eighteen days have passed this month" and they still had not received their rations. They were forced to buy their own wheat. They told them to send to the Pharaoh or Vizier to address their concerns. After the authorities had heard their complaints they addressed them and the workers went back to work the next day. There were several strikes that followed. After one of them, when the strike leader asked the workers to follow him they told them they had had enough and returned to work. This was not the last strike but they soon restored the regular wheat supplies and the strikes came to an end for the remaining years of Ramesses III.

I am not sure that it is the first case, but an ancient example is the Boston Tea Party protest:

On December 16, 1773, after officials in Boston refused to return three shiploads of taxed tea to Britain, a group of colonists boarded the ships and destroyed the tea by throwing it into Boston Harbor.

It followed with 8 long years of war and ended with the declaration of independence of the USA.

But I am almost sure that it is possible to find more ancient examples.

As nonviolence of the Tea Party has been challanged, I am adding another answer.

In Johannebourg, South Africa, September 11, 1908 Gandhi lead a non-violent protest of indians against Asiatic Registration Act.

This plan was adopted, leading to a seven-year struggle in which thousands of Indians were jailed (including Gandhi himself on many occasions), flogged, or even shot, for striking, refusing to register, burning their registration cards, or engaging in other forms of non-violent resistance. While the government was successful in repressing the Indian protesters, the public outcry stemming from the harsh methods employed by the South African government in the face of peaceful Indian protesters finally forced South African General Jan Christiaan Smuts to negotiate a compromise with Gandhi. He did eventually release him.

Going out on a limb here, and feel free to disagree, but what about the growth of the early Church?

The growth of the Church in early centuries was a form of independence movement, inasmuch as early Christians simply wanted to practice their faith without fear of persecution. Also, the growth of the church (emphasis on the small "c"), meaning the local communities, is by its very nature non-violent. One could make a very strong case that the activities of the Church (the Vatican) does not fit in that category because of the Crusades, among other reasons, but I'd say that the church as a community of believers is rather closely aligned with a non-violent independence movement.

Again, just a thought.